## Accounting for Joint Ventures Questions and Answers

Accounting For Joint Very Short Answer Type Questions

Question 1.
Define joint venture?
Answer:
It is an agreement between two or more parties called co-ventures, to undertake a particular venture or business and to share the profit or loss of that venture in a agreed ratio. It is a temporary partnership without a firm name or common name.

Question 2.
Write any four features of joint venture?
Answer:

1. the minimum member of persons required for a joint venture is two and there is no maximum limit on the number of parties
2. the persons who formed joint venture are called ventures or co-ventures.
3. The ventures contribute capital and managerial services for the joint venture.
4. It is temporary partnership without firm name of common name.

Question 3.
Write two differences between joint venture and partnership?
Answer:

1. a joint venture does not have a firm name or common name. but a partnership ha a firm name.
2. a joint ventures is restricted to a particular venture or business. But a partnership is not restricted to a particular venture or business.

Question 4.
Write two differences between joint venture and consignment?
Answer:

1. In a joint venture, there is temporary partnership. But in a consignment there is no partnership
2. In joint venture all the venturers are the owners of the business. But in a consignment only consignor is the owner of the business.

Question 5.
How do you treat goods supplied by a co-venture from his own stock?
Answer:
The goods supplied by a ventures to joint venture out of his own stock at cost or at selling price should be debited to joint venture account and credited to concerned ventures account.

Question 6.
What is meant by memorandum joint venture account?
Answer:
It is combination of joint venture with co-ventures accounts prepared in the books of each of the co-venturers. It is prepared to find out profit or loss on joint venture.

Question 7.
What is the journal entry for supplies of goods from co-ventures own stock?
Answer:
Joint venture with co-ventures a/c Dr
To concerned ventures a/c

Question 8.
What is the journal entry when any venture takes over the goods?
Answer:
Concerned ventures a/c Dr
To joint venture a/c

Question 9.
What are the objections of joint venture?
Answer:

1. To purchase and sale of goods.
2. To speculation of shares and debentures.
3. To underwrite the shares and debentures of a company.
4. To construction of buildings.

Question 10.
Why a joint venture is called as temporary partnership?
Answer:
A joint venture is formed between the ventures for a specific persons and it ceases to exit on the completion of the specific venture, so a joint venture is called temporary partnership.

Question 11.
State the methods of accounting for Joint ventures.
Answer:

1. When on co-venture keeps the record of joint ventures.
2. When all the co-venture keeps the record of joint ventures.
3. When a separate set of book is maintained for joint ventures.
4. Memorandum joint venture méthod.

Question 12.
When is a Memorandum Joint-Venture Account opened?
Answer:
This account is prepared to know the profit or loss on joint venture. it is merely combination of personal accounts. This account is debited with all items which are already debited in personal accounts.of all the Co-ventures. This account is credited with all items which are already credited in personal accounts of all Co-venturers. This differences in this account is treated as profit or loss.

Accounting For Joint Short Answer Type Questions

Question 1.
What are the differences between joint venture and partnership?
Answer:
Joint venture :

1. It does not have a firm name or common name.
2. It is restricted to a particular venture or business.
3. It is a temporary concern.
4. It is for a shorter duration.
5. The persons carrying on business are called co-venturers.
6. Accounts are prepared on closing of the joint venture.
7. There is no limit on the maximum number of co-ventures.
8. Co-ventures of a joint venture do not have implied authority.

Partnership :

1. It has firmi name.
2. It is not restricted to a particular venture or business.
3. It is a going concern.
4. It is for a longer duration.
5. The persons carrying on business are called partners.
6. Accounts are prepared annually.
7. There is a limit on maximum number of partners…
8. Partners of a firm have implied authority.

Question 2.
What are the differences between joint venture and consignment?
Answer:
Joint venture :

1. It is a temporary partnership.
2. The relationship between venture is that of partners.
3. All the ventures are the owners of the business.
4. All the ventures may buy and sell the goods.
5. A venture is not allowed to any commission on sales.
6. The finance is contributed by all the ventures.
7. All the ventures share the profits or losses in an agreed proportion.
8. It is governed by partnership act.

Consignment :

1. There is no partnership in consignment.
2. The relationship between consignor and consignee is that of principal and gagent.
3. Consignor is the owner of the business.
4. Only consignor buys the goods and consignee sells the goods.
5. The consignee is allowed to any commission or sales.
6. The finance is contributed by only the consignor.
7. The entire profit or loss go to consignor.
8. It is governed by the law of agency.

Question 3.
A & B enter into joint venture. A agrees to bring in cash are capital accordingly a joint bank account was opened by A for 80,000. B buys goods worth 50,000 as part of his capital. Further goods worth 1,18,000 were purchased from C paying 60,000 and balance by a promissory note signed by A & B.
The goods were sent to Davangere for sale. Expenses totalling 5,000 were incurred on sending the goods. Part of the goods were damaged in transit and a sum of 25000 were recovered from insurance company, the reaming goods were sold for 2,20,000.
Pass journal entries in common books assuming that the promissory note was duty honoured.

Question 4.
AB and entered into a joint venture and agreed to divide profits as A – 60%, B-305 and C-10%. They purchased by Auction several new machines for 50,000. A contributed 30,000, B 20,000 and C 10,000, for carrying on transactions relating to venture. A joint bank account was opened. The ventures were successful in selling the machines for 1,25,000. Excepting one machine which had to be scrapped and it fetched 750 only. A spent 2,450 and two other ventures spent 1,250 each in connection with the venture.
Prepare joint venture a/c and ventures accounts.

Question 5.
A and B agreed to import timer into India. They opened a joint bank account with 25,000 towards which A contributed 15,000 and B 10,000. They A agreed to share profits and losses in proportion to their cash contributions. They remitted to their agent 20,000 to pay for timber purchased and later 2100 insettlement of his account. Freight insurance and dock charges were paid in India which amounted to 3,900. The sales amounted to 28,740 which enabled him to repay themselves and cash originally advanced. They then decided to close the venture and B agreed to take over the balance of timber unsold for 1,260 which is to be deducted from his share of profit.
Prepare joint venture a/c and ventures a/c.

Question 6.
A and B entered in to a joint venture sharing profits and losses in the ratio of 3:2. They opened a joint account by depositing 40,000 each.
A purchased 800 kgs of A grade Tea at 60 per Kg and his expenses were 13,000. B purchased 400 kgs of B grade tea at 55 per kg. and his expenses were 11,000. Expenses were met from private sources and purchases were met from joint bank account.
B sold 600 kgs of A grade tea at 100 per kg and his selling expenses were 5,500: A sold 300 kgs of B grade tea at 110 per Kg and his selling expenses were 6m000. All the proceeds were deposited in the joint bank account and expenses were met by private sources.
Prepare joint venture a/c and ventures a/c.

Question 7.
X and Y entered into a joint venture sharing profit and loss in the ratio of 3:2.X supplied goods to the venture worth 10,000 and incurred expenses 1,000. Y also supplied goods valued 8,000 and paid 500 for expenses.
X and Y sold on behalf of the venture realized 16,000 and 12,000 respectively. They are entitled to get a commission at 10% on their respective sales.
Un sold goods valued 1000 were taken over by X and Y in their profit sharing ratio.
Show ledger accounts in the books of X.

Question 8.
Ajay and Vijay entered into a joint venture in timber business Vijay is allowed a commission on sales at 10% and profits are to be shared in the Ratio of 2:1. Ajay provides timber from stock for 10,000 and incurs expenses amounting to 1000. Vijay pays 1000 for unloading and other non-recurring expenses. Ajay drew on Vijay for 6000. The draft was accepted and Ajay got it discounted for 5,760. Vijay sold 90% of the timber for 15,000 and took over the remaining timer at cost plus 20% and settles his account by Bank draft.
Write joint venture account and Vijay’s account in the books Ajay.

Question 9.
Veena and Meena entered into a joint venture sharing profits and losses in the ratio of 3:2. Veena contributed Rs. 60,000 and Meena Ks. 80,000. The amounts contributed by them were deposited into a joint bank account. They bought goods for cash Rs. 1,00,000 and from Veena for Rs. 40,000. They paid for carriage Rs. 7,000, Rent Rs. 2,000, insurance Rs. 3,000 and other expenses Rs. 4,000. All the goods were sold for Rs. 1,80,000.
Pass the necessary journal entries.

Question 10.
Deepa and Eswari entered into a joint venture to purchase stationeries and supply them to colleges. They agreed to share profits in the ratio of 5:3 and to maintain books of accounts for the joint venture under memorandum Joint Venture Method.
Deepa and Eswari purchased stationeries for Rs. 6,00,000 and Rs. 4,50,00 respectively and sold them for Rs. 7,50,000 and Rs. 5,25,000 respectively. Selling expenses incurred by them are Rs. 35,000 and Rs. 25,000 respectively. No goods remained unsold and the final amount is settled by cheque.
Prepare necessary accounts in the books of Deepa.

Question 11.
Kavitha and Kalpana are entered into a joint venture sharing profits and losses in the ratio of 3:2 Kavitha contributes Rs. 1,20,000 and Kalpana Rs. 1;60,000. The amount contributed by them were deposited into a joint bank account. They bought goods for cash Rs. 2,00,000 and from Kavitha for Rs. 80,000. They paid for carriage Rs. 15,000. Rent Rs. 4,000 Insurance Rs. 5,000 and other expenses Rs. 9,000. All the goods were sold for Rs. 3,50,000
Pass necessary journal entries.

Question 12.
Radha and Sowmya entered into a Joint – Venture to buy and sell goods and share profits and losses equally. They opened a Joint Bank Account to which Radha contributed Rs. 55,000 and Sowmya contributed Rs. 50,000. Radha and Sowmya purchased goods for Rs. 1,05,000. Radha also supplied goods worth Rs. 7,500 and paid rent for the venture Rs. 1,500. They sold goods for Rs. 1,60,000. The expenses incurred on advertisement amounted to Rs. 4,000 which were paid by Sowmya and she took balance of stock for Rs. 3,000.
Prepare Joint Venture Account in the books of Radha.

Question 13.
Praveen and Karthik were partners in a joint venture sharing profits and losses equality. Praveen supplied goods to the value of Rs. 20,000 and incurred expenses amounted to Rs. 1,600. Karthik supplied goods to the value of Rs. 16,000 and his expenses amounted to Rs. 1,600. Karthik sold the entire goods on behalf of the joint venture and realized Rs. 48,000. Karthik was entitled to a commission of 5% on sales. Praveen settled his account by bank draft.
Show the Ledger Accounts in the books of Praveen and Karthik under Memorandum Joint Venture method.

Question 14.
Naveen and Praveen entered into a joint venture to construct a building for Rs. 7,50,000. Naveen and Praveen contributed Rs. 3,75,000 and Rs. 2,85,000 respectively. They agreed to share profits and losses in the ratio of 3 : 2. It was i decided that the work would be looked after by Naveen, who would be paid 10% commission on contract price in addition to his share of profits. Naveen bought the necessary materials for Rs. 6,00,000 and paid Rs. 18,000 for expenses. He also contributed building materials from his own stock worth Rs. 37,500. There was an outstanding wages of Rs. 9,000.
The building was completed and the contract money was duly received. Praveen took over the stock of materials at an agreed value of Rs. 30,000 and outstanding wages were paid by Naveen.
Prepare Joint Venture A/C and Praveen’s A/c in the books of Naveen.

Accounting For Joint Long Answer Type Questions

Question 1.
XYZ jointly under took to construct a building for Patil and Co., at a price of 2,50,000. The price was to be paid as follows.
2,00,000 in cash and the balance in preference shares of the company. Profit was agreed to be divided in the Ratio 2:2:1. The participants contributed cash as follows X – 30,000, Y – 25,000 and Z-20,000. These amounts were credited to a joint bank account. Y was to be paid a remuneration of 1500 for managing the business.
X prepared the plans and paid 3500 for them. Y brought concrete mixed for 12,000 and Z brought a truck for 25,000. They brought plant for 15,000, materials 1,20,000 and wages 1,05,000.
When contract was completed X took over unused materials for 10,000, Y took back concrete mixer for 11,000 and Y agreed to take back the truck 18,000. The plant was sold as scrap for 6,000.
When the contract price was received. X agreed to take over the preference shares for 40,000. All the accounts were closed. Pass journal entries assuming that the accounts are finally settled among the partners.

Question 2.
A, B and C enter in to a joint ventures to divide profits equally. They bought goods from smart and Co.for 12,500 and from Xher 2,500. X contributed 3,000, Y-4,000 and Z-9,000 which amounts where banked in a joint account. They settled their accounts with smart and Co. by cheque and paid for carriage and other expenses 750. They sold goods by cash 6,500 and to Smit and son on credit for 14,000 who accepted a draft for the amount. The acceptations was cashed and realized 13,700. X was allowed 5% commission on sales for effecting the from tranctions.
Prepare necessary accounts, assuming that final settlement between parties was made by cheques.

Question 3.
Arun and Varun entered into a joint venture for dealing in second hand cars. It was agreed that Arun should buy cars that Varun should attend to the reconditioning of them. That a commission of 5% should be allowed on sale made by each and that profits and losses should be divided equally.
Arun purchased 7 cars for 18,500 and paid 210 fro insurance and 130 for advertising. Varun contributed 3000 for the purchase money and paid for repairing – batteries 180 for repairing types 330 and for repairs 630 and charged 1000 for garaging the cars.
Arun sold 2 cars for 6,600 and Varun sold 4 cars for 13,360. Arun took over the remaining car at 2,900 and the venture was closed.
Show ledger accounts of the venture in the books of each party.

Question 4.
A and B entered in to a joint venture sharing profits and losses in the ratio of 3:2 X supplied goods to the venture worth 20,000 and incurred expenses 2,000 Y also supplied goods valued 16,000 and paid 1,000 for expenses.
X and Y sold goods on behalf of the venture and realized 32,000 and 24,000 respectively, They are entitled to get a commission at 10% on their respective sales.
Unsold goods valued 2000 were taken over by X and Y in their profit sharing ratio.
Show ledger accounts of the venture in the books of each party.

Question 5.
A and B enter into a joint venture to consigin 100 sales to C to be sold on their joint stock. They agree to share profits or losses equally.
A sent 50 bales valued at 60,000 and pays fright and expenses 1200. B sent 50 bales valued at 55,000 and paid expenses 900.
All the bales reached to Kolkotta in time. However 5 bales were found to have tampered with during the transit. A recovered 3000 from insurance company. C sold the remaining bales for 1,35,000. He chared 3% as selling commission and deducted 1,500 towards expenses. He remitted the balance to A by DD on SBI of India payable at Ahmedabad.
Prepare necessary accounts in the books of both parties assuring that each venture records in his books only the joint venture transactions effected of him.

Question 6.
M and N decided to work the following scheme in partnership agreed to share profits as 3 : 2 ratio.
They guaranteed the subscription at par of 10,00,000 shares of 1 each in the Vijaya Ltd., And to pay all expenses upon allotment in consideration of the Vijaya Ltd., issuing to them 1,00,000 other shares of 1 each.
Mintroduced cash in to the business to meet the following expenses
Stamp charges and registration fees – 4,000
Advertising charges – 3,000
Printing charges of MOA, AOA and prospectus – 3,000
N introduced cash to meet the following expenses, Rent – 2,000
Solicitors charges – 3,000
The application fell short of the 10,00,000 shares by 20,000 shares. N introduced further cash on joint account for the said 20,000 shares. This amount was utilized to the said 20,000 shares and paid to the company.
The guarantee having been fulfilled, the Vijaya Ltd. Handed over to M & N 1,00,000 shares. The partnership sold all the shares. N received the sale proceeds of 80,000 share amounting to 60,000 and M of the remaining 40,000 shares amounting to 25,000.
Give the necessary accounts in the books of each venture to record his own transactions assuming that final settlement by made between the ventures.

Question 7.
Rajesh, Satish and Mahesh Entered into a joint venture according to which Rajesh and Satish purchase goods and send the same to mahesh who is a marketer. Mahesh would sell the goods for a commission of 10% Rajesh and Satish agreed to share the remaining profit in the ratio of 3:2. Rajesh purchased goods for Rs. 1,00,000 and sent them to Mahesh incurring an Expenditure of Rs. 4,000. Satish purchased goods for Rs. 60,000 and sent the same to mahesh by incurring an Expenditure of Rs. 3,000.
Mahesh Exported all the goods and realised Rs. 2,00,000, by paying Rs. 1000 as insurance premium. He also received Rs. 8,000 as insurance compensation for some goods destroyed.
Mahesh paid the balance of cash to Rajesh and Satish.
Prepare:
a) Memorandum Joint venture account
b) Co-ventures accounts.

Question 8.
Jayanth, Kumar and Lakshman entered into Joint Venture and agreed to share profits and losses in the ratio of their capital contributions. They contributed Rs. 2,50,000, Rs. 1,50,000 and Rs. 1,00,000 respectively into the Joint Bank Account. The purchases and sales were as follows:
Credit purchases from A Ltd. Rs. 5,00,000
Credit purchases from B Ltd., Rs. 3,00,000
Cash purchases from C Ltd., Rs. 4,00,000
Cash sales Rs. 9,00,000
Credit sales to C Ltd., Rs. 6,50,000
Office expenses Rs. 30,000. The unsold goods were taken over by Kumar at an agreed value of Rs. 20,000. Lakshman is entitled to a special commission of 5% on gross sales. all balances were settled through Joint Bank Account at the end.
Prepare:
a) Joint Venture A/c
b) Joint Bank A/C
c) A Ltd. Alc
d) B Ltd., A/C
e) C Ltd., A/c and
f) Co-ventures’A/c

Question 9.
Akash and Ashwin undertook a joint venture for construction of a college building. A joint bank account was opened in which Akash deposited Rs. 2,00,000 and Ashwin Rs. 50,000. The contract price was Rs. 10,00,000. The profit of joint venture was to be shared as to Akash 2/3 and Ashwin 1/3.
The details of the transactions are as follows:
Rs.
Salaries – 30,000
Wages – 1,80,000
Materials supplied by Akash – 35,000
Building materials purchased – 4,00,000
Materials supplied by Ashwin – 35,000
Architect’s fees – 25,000
Carriage – 45,000
Machinery purchased – 80,000
On the completion of the contract the unused materials of the value Rs. 40,000 were taken over by Akash. The machinery was sold for Rs. 60,000. Mr. Ashwin was to be paid a remuneration of Rs. 30,000 for his service which is to be charged to the joint venture.
Prepare the necessary ledger account.

Question 10.
M, N and O enter into a joint-venture and decided to divide profits/losses equally. they bought goods from Suvarna and Co. for Rs. 4,00,000 and from ‘A’fro Rs. 50,000 and spent Rs. 4,500 as carriage. M contributed Rs. 1,10,000, ‘N’ Rs. 1,50,000 and ‘O’Rs. 2,00,000 which were deposited into a joint bank account. they paid Rs. 50,000 to Mr. ‘A’and Suvarna and Co. received Rs. 3,96,000 for full settlement of their account. they sold for cash Rs. 95,000 and to Z Co. on credit Rs. 4,55,000. The amount due from ‘Z’Co. received fully. ‘M’ was allowed 5% commission on sales for effecting the transactions.
Prepare the necessary ledger accounts.

Question 11.
Das and Boss entered into a joint venture sharing profits and losses as 3:2. They opened bank a/c by depositing Rs. 40,000 each. Das purchased 800 kg. of an item @ 60 per kg. and his expenses were Rs. 13,000. Boss purchased a second item of 10,000 kg. @ 2.10 per kg. and his expenses were Rs. 11,000. Expenses were met from private sources and purchases were paid from bank account. Boss sold 600 kg. of the first item @ 100 per kg. and his selling expenses were Rs. 5,500. Das sold Rs. 8,000 kg. of second item at Rs. 5 per kg and his selling expenses were Rs. 6,000. All the sale proceeds were deposited in bank account and expenses were met from private sources.
Write up necessary accounts in the books of the joint venture.

Question 12.
Charith and Chinmay entered into a joint venture and agreed to share profits and losses in the ratio of 3:2 after providing for interest on capital at 10% p.a. A joint bank account was opened in which Charith deposited Rs. 4,00,000 and Chinmay deposited Rs. 2,00,000 on 1.4.2017. goods purchased for Rs. 3,75,000 in cash and was sent to Bengaluru agent for sale.
Freight and insurance amounted to Rs. 7,500 was paid. All the goods were sold by the agent for Rs. 7,00,000. The agent remitted the balance amount after deducting his commission at 3% and expenses of Rs. 4,000.
Prepare :
a) Joint venture A/c,
b) Co-venture’s A.c,
c) Joint Bank A/c and
d) Agent’s A/c in the books of joint venture.

## Consignment Accounts Questions and Answers

Consignment Accounts Very Short Answer Type Questions

Question 1.
Who is consignee?
Answer:
The agent to whom goods are consigned by the principal for sale in return for commission is called the consignee.

Question 2.
What is mean by consignment.
Answer:
Dispatch or sending of goods by a principal to his agent at home or aboard for sale on his behalf and at his Risk in return for commission is known as consignment transaction or consignment.

Question 3.
What is Del-Credere commission?
Answer:
The extra commission payable by the consigner to the consignee for the consignees speciali services (i.e. his under taking the risk of bad debts arising out of credit sales) is called del credere commission. It is calculated at a fixed percentage on total sales or on credit sales.

Question 4.
What is meant by over riding or special commission?
Answer:
The additional commission paid over and above the ordinary commission is called overriding commission or special commission the objective of this commission is to give on incentive to the consignee to the goods at a price higher than the invoice price.

Question 5.
What is meant by proforma invoice?
Answer:
When consigner consigns goods to consignee, the consignee does not prepare a regular invoice but he prepares and sends to the consignee a statement which is similar to invoice. Such a statement is called proforma invoice.

Question 6.
What is meant by account sales?
Answer:
Either on the completion of the sales of periodical intervals the consignee sends goods to consigner on account of the goods sold by him in the form of a statement such a statement is called on account sales. This statement constitute an evidence of the amount due from the consignee to the consignor.

Question 7.
What is consignment stock?
Answer:
If the consignee has not been able to sell the goods sent to him by the consigner by the close of the consigners accounting period, the goods that remain unsold with the consignee on the closing date are the called consignment stock.

Question 8.
How is consignment stock is treated?
Answer:
The consignment stock can be brought in to the consignment account by debiting the consignment stock account and crediting the consignment account.

Question 9.
Give four examples of recurring expenses incurred by consigner?
Answer:

1. Discount charges on discounting bills of exchange.
2. Bank charges for realigation of bills of exchange.
3. Expenses incurred on goods returned by consignee.
4. Bad debts to be borne by consigner.

Question 10.
Give four examples of recurring expenses incurred by consignee?
Answer:

1. Godown rent
2. Loading insurance
3. Advertisement
4. commission

Question 11.
Give four examples of the receiving expenses incurred by consigner?
Answer:

1. Package charges
2. Leading charges
3. Carriage
4. Freight

Question 12.
Give four examples of non-recurring expenses incurred by consignee?
Answer:

1. Import or customs duty
2. Dock dues
3. Unloading charges
4. Railway charges

Question 13.
How is consignment stock is valued?
Answer:
For the purpose of bringing the consignment stock in the consignment account, the consignment stock has to be valued on the basis of cost price or market price which ever is lower.

Question 14.
How do you treat goods sent as consignment used for advertisement?
Answer:
The value of goods distributed by consignee as free samples should be dedited to advertisement account and credited to consignment account in order to known the real profit or loss as consignment. Again the advertisement can be treated as an expense for a particular consignment.

Question 15.
How do you treat loss of stock by accident.
Answer:
Loss of stock by accident is a abnormal loss, so they should not be charged co consignment account instead they should be charged to profit and loss account.

Question 16.
How do you treat loss of consignment stock by natural causes? [May/June 2013]
Answer:
Loss of consigument stock by natural causes treated as normal loss which arises due to Evaporation, Leakage, Shrinkage, breakage etc., There is no separate entry in the consignment account for normal loss. They are directly taken into account by adjusting it in the cost of or value of the unsold stock.

Question 17.
What are the difference between invoice and proforma invoice.
Answer:
Invoice:

1. It is prepared by seller when goods are sold.
2. It serves as a evidence of sale.
3. It is regular and real sale invoice.
4. It acts as a record for making entries in the books of accounts.

Proforma invoice :

1. It is prepared by consigner when gods are consigned to his consignee.
2. It service as a evidence of consignment.
3. It is not regular and real sale invoice.
4. It doesnot act as a record for making entries in the books of accounts.

Question 18.
What are the differences between profarma invoice and account sales?
Answer:
Profarma invoice :

1. It is sent by consigner to consignee.
2. It is sent only once along with the goods sent.
3. It does not make the consignee responsible to pay the amount stated.
4. It does not serve as basis of accounting entries.

Accounts sales :

1. It is sent by consignee to consigner.
2. It is sent on completion of sales or periodically.
3. It make the consignee responsible to pay the amount stated.
4. It serves basis of accounting entries.

Question 19
Give the meaning and example for non-recurring expenses in consignment accounts.
Answer:

1. Import or customs duty
2. Dock dues
3. Unloading charges
4. Freight charges.

Question 20
What is Account Sales?
Answer:
An account sale is a statement prepared and sent by the consignee to the consignor. It contains the details with regard to the quantity of goods received, sales made, expenses incurred, commission amount sent and the balance payable by consignee to the consignor.

Consignment Accounts Short Answer Type Questions

Question 1.
Distinguish between sale and consignment.
Answer:
Difference between sale and consignment –
Sale :

1. The ownership of the goods sold passes from the seller to the buyer.
2. Actual delivery of the goods may or may not be given to the purchaser.
3. The risk connected with the goods goes to the buyer.
4. Goods once sold cannot be returned by the buyer of seller.
5. The relationship between the seller and buyer is that of creditor and debtor.
6. The buyer can take care of the goods purchased in any way he likes.
7. The buyer can dispose of the goods in any way he likes.
8. Goods are supplied by the seller to buyer only against the buyers order.

Consignment :

1. The ownership of the goods consigned remains with the consignor.
2. The consignee gets the actual deliver of the goods.
3. The risk connected with goods lies with the consignor.
4. Unsold goods can be returned by consignee to the consignor.
5. The relationship between the consigner and consignee is that of principal and an agent.
6. The consignee has to take reasonable care of the goods consigned.
7. The consignee has to dispose of the goods exactly in the manner prescribed by the consigner
8. Goods may be sent by the consigner to the consignee even if there is no order from consignee.

Question 2.
Excel chemicals ltd. Consigned to National Chemicals Co. 2000 kgs of a chemical the cost of chemical and fright there on were 18 and 1 per kg respectively. An account sales was received from the consignee showing 1000 kgs where sold of 32 per kg. sales expenses amounted to 1 per kg insurance 1000 brokerage at 10% and consignee commission at 2 1/2 %. They also reported a shortage of weight of 40 kgs on the whole consignment which was due to the inherent quality of the chemical.
Show the consignment account and consignees a/c in the books of consignor.

Question 3.
Azar consigned 100 cases of goods to Sachin to be sold in his risk. The cost of one case of goods was 150. Azar paid freight 700 and insurance 300. Sachin sent on account sales showing that 80 cases were sold at 220 each. Expenses incurred by sachin were carriage 100 godown rent 500 and advertisement 300. He is entitled to commission of 5% on sales.
Proper consignment account and consignees a/c.

Question 4.
1000 bicycles were consigned by Roy of Kolkatta to Noy of Bangalore at an invoice cost of 150 each. Roy paid fright 10000 and insurance 1500. During the voyage 100 Bicycles were totally damaged by fire and had to be thrown overboard.” Noy took delivery of remaining bicycles and paid 14,400 for customs duty. Noy sent a bank draft to Roy for 50,000 as advance and sent an account sales showing that 800 bicyles were sold at 220 each. Expenses incurred by Noy on go down rent and advertisement amounted to 2000. Noy is entitled to a commission of 5% on sales. Assuming that nothing was recovered from insurance due to a defect in policy prepare consignment account and consignees a/c.

Question 5.
Ramu consigns to Vishnu 40 cases of goods at a cost of 5000 per case and incurs the following expenses in connection with the same viz. cartgage 940, freight 3480 and insurance 12,500. On arrival of the goods Vishnu pays cleaning charges 3,120, cartage 960 and go down rent 200. Six cases are destroyed by the fire and a sum of 30,000 is realized from the insurance company by way of compensation. Out of the remaining 34 cases, 24 cases are sold at a total price of 2,20,000. Vishnu is entitled to an ordinary commission of 5% and 2% del credere commission on sale in addition to reimbursement of expenses incurred. He sends to Ramu an account sales together with a bank draft for the balance due to Ramu. In the books Ramu show consignment a/c and Vishnu a/c.

Question 6.
Mr. Ashok dispatched 100 tea boxes costing 150 each at 20% above cost their special agent Mr. Kumar of Poona. He paid 500 for package and 200 for other expenses. He draws as advance bill of 5,000 for 4 months and the same was discounted at 6% p.a. with bank.
100 for unloading
50 for carriage to go down.
Consignee sold 60 boxes at 210 each and 20 boxes at 200 each. He is entitled to commission 10% as sales and 2% special commission and he has to bear all expenses himself Kumar remitted the balance by bank draft. Empty boxes were sold her 200.
Show consignment account and consignees account in the books of consignor.

Question 7.
Ravi of Bangalore sent a consignment of 2000 articles to his agent Sridhar of Kolar at Rs. 20 per article. Railway charges, cartage and Insurance amounted to 10 % of total cost of goods. Sridhar sold 2000 articles at Rs. 30 each and sent an account sales enclosing a bank draft for the balance after deducting
a) his advance of Rs. 5,000
b) his expenses Rs. 500 and
c) his commission at 10% of Gross sales.
Pass the necessary Journal Entries in the books of Ravi of Bangalore.

Question 8.
Bhaskar consigns 1,200 units of a product costing Rs. 300 each to Chandan. He incurs Rs. 6,000 for carriage expenses. 60 units of the product are stolen in transit. Chandan receives the remaining goods, and sells 1,020 units at Rs. 460 per unit. Expenses incurred by him amounted to Rs. 4,260, the entire amount being non-recuring. He reports a normal loss of 24 units. Find the value of abnormal loss and closing stock.

Question 9.
Lokesh of Mysore sends 2000 Kgs of oil at Rs. 120 per kg to Nataraj at Hubli. The consignor spends Rs. 11,000 on cartage, insurance and freight. On the way 100 Kgs of oil was lost (normal loss) due to leakage and evaporation. Nataraj took delivery of the consignment and spent Rs. 9,000 on octroi and carriage. His selling expenses were Rs. 7,000 on 1700 Kg of oil sold. Determine the value of stock.

Question 10.
Mr. Nandish of Mysore, consigned 500 kgs. of oil @ Rs. 30 per Kg. to Mr. Satish. He paid Rs. 4,000 as carriage and freight charges. Mrs. Satish also paid Rs. 1,000 towards unloading charges Rs. 2,000 as godown rent and Rs. 1,500 as selling expenses. Normal loss due to leakage is 40 kgs. of oil in transit. Satish sold 320 kgs. of oil @ Rs. 55 per Kg. and 19 Kgs. of oil @ Rs. 60 per kg.
Calculate value of unsold stock.

Question 11.
Krishna Murthy of Bengaluru sent a consignment of 2,000 articles to his agent Sri Raghavan on Tumukur at an invoice price of Rs. 20 per article. Railway charges, cartage and insurance amounted to 10% of the total invoice price. Raghavan sold 1,500 articles at Rs. 30 each and sent an account sales enclosing a bank draft for the balance after deducting
i) his advance of Rs. 5,000
ii) his expenses Rs. 500 and
iii) his commission at 10% on gross sales. 100 articles were lost in transit and the insurance company admitted the claim for Rs. 1,100. Show the Consignment Account and Consignee’s Account in the books of the Consignor.

Question 12.
Calculate the value of abnormal loss and value of closing stock from the following information:
a) Goods sent on consignment – 400 units of glassware at Rs. 100 unit.
b) Expenses incurred by the consignor – Rs. 2,000.
c) Goods lost in transit – 20 units.
d) Expenses incurred by the consignee – taxes Rs. 1,420 and selling expenses Rs. 1,000.
e) Goods sold by the consignee – 340 units.
f) Goods damaged at Consignee’s place – 2% of the total goods consigned (which is permissible)

Consignment Accounts Long Answer Type Questions

Question 1.
ABC Ltd. Davangere consigned 100 bicyles to XYZ Bangalore invoiced at 350 each, the invoice price was made by adding 25% to the cost on sending the goods ABC Ltd. Paid freight 2000 and insurance 1000. During transit to bicycles were totally damaged by fire and the insurance Co. paid. 2000 directly to the consignors in bill settlement of the claim.
XYZ Ltd. Took delivery of the remaining bicycles and paid 1000 towards octroi charges and 800 towards cartage. They sent a bank draft for 25.000 and later on account sales showing 75 bicycles were sold t 480 each. Expensed of XYZ Ltd. On godown rent and adverting amounted to 1500, They are entitled to a commission of 6% and 25 declrede.
Assuming that the consignee paid the amount by bank draft show the necessary ledger accounts in the books of ABC Ltd.

Question 2.
The Lakshmi Radio Co. Ltd., of Delhi dispatched 1000 Radio set costing 600 each to Nayak & Co., o Mangalore on 25th March 2010. The Lakshmi Radio Co., Ltd. incurred the following expenses on consignment.
Fright 7500, cartage 500 and insurance 2000. The profarma invoice to the agents was for 90,000 and the remuneration was fixed at 5% on gross sales. The agents accepted a bil for 2,00,000 drawn on them as an advance.
On 30th June 2010, 100 Radio sets were totally destroyed by fire and 9,000 were duly received by consignor from insurance in full settlement of the claim. On 31st December 2010 the company received on a account sales from the agent showing’ that 600 radio sets were sold for 6,00,000 and they paid customs 1,00,000 duck dues and clearing charges 5,000, were warehousing and insurance 4,500, sales expenses 6,000 and commission 30,000.
The agents remitted a draft for the balance due to consignor. It was reported by the agents that some of the sets had got damaged and the cost of putting them in repairs was estimate at 6,000.
Prepare the necessary account in the books of Lakshmi Radio Co. Ltd.,

Question 3.
Shakthi of Suresh sends consignment of goods to Bhakthi of Mumbai and charges of proferma invoice price so as to show profit of 33 1/3% on cost, the agent receive commission at 7% plus 3% Delcredere Commission on all sales made by him.
During the year 31st December 2011 Shakthi had the following transaction with Bhakthi.
a) Proforma invoice price of 100 cases of goods consigned to Bhakthi 60,000
b) Advance received from Bhakthi 25,000
c) Freight and insurance paid by Shaktihi 2,000
d) Sales made by Bhakthi
(i) 40 cases for cash 30,500
(ii) 40 cases for credit 52,000
e) Selling expenses paid by agent 1800 and discount allowed by him 800
f) Owing to faulty packing 10 cases of goods were damaged and a claim on the underwriters was settled by Shakthi for 1500
g) Out of goods sold on credit 1500 was irrecoverable and considered bad by the agent.
h) The agent remitted the balance due by him by a bank draft.
Show necessary ledger accounts in the books of both the parties.

Question 4.
Rao and Rao sent to their agents Kamat and Brothers a consignment of hides and sinks costing 24,000. They incurred 1200 on freight and packing and 500 towards insurance. They drew a 3 months bill on their agents for 20,000, it was accepted by agent. A commission of 5% and decredere commission at 1% was payable on sales to the agents.
It was found that due to faulty packing goods costing 2400 were damaged during transit and the insurer admitted the claim for 2000. However these damages goods were sold by the consignor for 1,250.
Half of the goods on consignment was sold for cash 14,600 the balance on credit for 18,200.
The agents had incurred landing and storage expense of 600 and 800 respectively out of the goods sold on credit 1200 was irrecoverable and considered bad by the agents.
Show ledger accounts in the books of both the parties.

Question 5.
A consigned to B on 1.1.2010, 500 bales of cotton costing 100 per bale, freight charges incurred on consignment were 5000. A drew a bill on B for 50,000 payable on 30th June 2010 which B accepted. The bill was discounted by a with his banker on 31st January 2010 at 12% p.a.
B rendered account to A on 31st March 2010 showing sales of 300 bales for 80,000 and selling expenses 5,000. B’s commission was 10%. On this date b remitted A the net amount due to him.
On 31st May 2010 B sold the balance stock for 30,000 and spent selling expenses 4,000. He remitted 20,000 to A, the balance being treated as commission earned by him. On 30th June 2010 the bill accepted by b was dishonoured by him and the amount due to bank was paid off by a long with incidental charges of 200.

Question 6.
B of Bangalore consigned 100 Radio sets costing 500 each to D of Davangere the invoice was made at cost plus 20%. D was entitled to a commission of 7%2% (including detcredere commission) and 10% of any profit that may remain on the basis of the invoice price. D was to bear all expenses incurred after the goods reached his godown.
While sending the goods B paid 1500 as forwarding expenses and insurance. In trasit 10 Radio sets were damaged and B recovered 4000 from insurance company. D took delivery of the remaining sets by paying 4500 as freight and carriage. D sold 70 Radio sets at 850 each, 30 of them on credit, out of which the process of 3 Radio sets were not recovered because of disappearance of a customer. He paid 1000 as storage and selling expenses. D set a bank draft for the amount due to B.

Question 7.
Atlas Cycle Co. Mysore forwards on 1.7.2011, 100 bicylces to Raju Cycles Mart, Mangalore to be sold on consignment basis. The cost of one cycle was 450 but invoice price was 600. Atlas cycle Co., incurred 3000 towards fright and insurance. Raju cycle mart gave an acceptance of 30,000 in followed atlas cycle Co., the acceptance was has 3 months. Atlas Co. discounted the bill at 10% p.a. Two cycle were destroyed in transit and an amounted 600 was required by the consignor from insurance company. Raju cycle mart had spent 1200 as rent and 750 as insurance and had sold 80 bicycles at 615 each. The consignee is entitled to a commission of 5% on sales including delcredere commission of 1%.
Raju cycle mart were not able to recover the sale process of 5 bicycles because of insolvency of debtor.
Prepare ledger accounts in the books of Atlas Cycle Co.,

Question 8.
Amco Batteries Ltd. Bangalore consigned 1,500 Batteries costing Rs. 5,000 each, to Manju Electricals of Mulbagal. The consignor paid Rs. 75,000 towards Freight charges and insurance Rs. 30,000. During transit it was found that 10 Batteries were damaged and insurance company settled the claim for Rs. 45,000. Manju Electricals received the balanced consigned goods and paid unloading charges Rs. 14,900. They accepted a bill drawn for Rs. 20,00,000 as advance. Manju Electricals sold 800 Batteries for cash at Rs. 6,500 and 450 batteries on credit at Rs. 7,000 each. They spent Rs. 42,000 for Godown Rent, Rs. 6,500 for advertisement and Rs. 30,000 as salesmen salary. The consignee entitled to get an ordinary commission at 5 % on sales and Del credere commission at 2 % on credit sales. Manju Electricals remit the balance due -signor by bank draft. Prepare (a) Consignment A/c (b) Consignee A/c (c) Abnormal Loss A/c.

Question 9.
Hamsa sends 70,000 units of a product at Rs. 40 each to Indira on consignment basis and incurs Rs. 16,000 on freight and Rs. 14,500 on agents commission. On receipt of goods Indira accepts a bill drawn by Hamsa for Rs. 6,00,000 for 3 months and at the end of the accounting year, she sends account sales showing the following details :
Sales – 60,000 units at an average price of Rs. 58 each.
Normal loss – 2% of the goods consigned.
Expenses incurred – Unloading charges Rs. 14,000, Carriage inwards Rs. 15,000 carriage outwards 12,500 and Godown Rent Rs. 13,500
Indira is entitled for a commission of 5% on total sales. The final balance due to Hamsa is settled by Bank Draft.
Pass journal entries and prepare necessary ledger accounts in the books of Hamsa.

Question 10.
M/s Raghu and Co. of Delhi consigned on 15th March 2012, 45 cases of glass at cost price Rs. 45,000 to Reddy and Co. of Hyderbad for sale on commission at 5% on gross sale proceeds. The consignor paid freight and carriage amounting to Rs. 539.
The goods arrived at Hyderbad on 20th March 2012, Reddy and Co. paid clearing charges Rs. 235, sundry charges Rs. 59, carriage Rs. 102 and godown charges Rs. 90.
The goods were sold by Reddy and Co. as under 15 cases at Rs. 1,000 per case, 22 cases at Rs. 1,050 per case and the remaining 8 cases at Rs. 1,250, per case.
On June 21, 2012, Reddy and Co. sent a draft for Rs. 10,000 to M/s Raghu’and Co. on account. On 1st July 2012, Reddy and Co. forwarded an account sales together with a Bill of Exchange for the balance.
Give journal entries to record the above transactions in the books of consignor and consignee. Calculations are to be made to the nearest Rupee.

Question 11.
M/s Sagar and company consigned 1500 tins costing Rs. 600 per tin to their agent Manohar Stores, Kolkata. The tins were invoiced at proforma price of Rs. 800 per tin. the agent sold 900 tins at Rs. 810 per tin for cash, 400 tins at Rs. 850 on credit. The Sagar and Co. paid Rs. 5,000 as freight and Rs. 2,000 as insurance. they drew a bill on Manohar stores at 3 months for Rs. 6,00,000 which was duly accepted by the latter, the expenses incurred by the Manohar stores were carriage Rs. 500, Octroi Rs. 1,500 and storage rent Rs. 1,100 they were entitled to 5% commission and 2% del-credere commission on total sales. They sent their account sales to their principal showing as a deduction there from their commission and the various expenses incurred by them.
Prepare necessary ledger accounts in the books of M/s Sagar and Co.,

Question 12.
Madan of Bengaluru consigns goods to Swamy of Davangere to be sold at or above invoice price. Swamy is to get 10% commission on sales at invoice price plus 20% of any surplus price realized. Madan draws on Swamy at 60 days bill for 80% of the invoice price the balance of the proceeds being remitted by the bank draft by Swamy after deduction of his commission immediately upon sale.
On 1st Jan. 2016 Madan consigned to Swamy goods whose total cost including freight was Rs. 1,50,000 the invoice price of which was Rs. 2,25,000. Sales by Swamy by 30th June 2016 amounted to Rs. 2,05,000. Goods unsold on 30th June 2016 with Swamy were of invoice price Rs. 65,500 (Cost including freight Rs. 45,000). On 30th June 2016 Madan had received from Swamy by the bank draft Rs. 49,750, certain remittances being in transit on 30th June 2016.
Show the Ledger Alc’s in the books of Madan recording the above transactions.

## Commercial Mathematics Questions and Answers

Commercial Mathematics Very Short Answer Type Questions

Question 1.
What is Discount?
Answer:
Discount is deduction from the price of the goods sold given by the seller to the purchaser. Ex.: If seller accepts Rs. 85 against the price of Rs. 100 in full settlement, then Rs. 15 is known as discount given by seller to buyer.

Question 2.
What are the types of discounts in business transactions.
Answer:
In business transactions the following types discounts are allowed.

1. Trade discount
2. Cash discount

Question 3.
What are the different types of discount in bill transactions.
Answer:
The bill transactions the following are considered.

1. Banker’s discount
2. True discount
3. Calculation of average due date

Question 4.
What is trade discount?
Answer:
Trade discount is a deduction from the list price or catalogue price of an article. This discount is allowed between wholesaler to retailer or manfactures to a wholesaler. The invoice price of an article is arrived at after deducting the trade discount.

Question 5.
What is cash discount.
Answer:
Cash discount is a deduction from the invoice price given for prompt payment within a specified period by seller to buyer. Thus Invoice price = List price – Trade discount .
Cash price = selling price – cash discount

Question 6.
Find the invoice price if the list price is Rs. 20,000 with trade discounts 20% and 10%.
Answer:
30% of 20,000 = 30/100 × 20,000 = Rs. 6,000
Then the price of the article = 20,000 – 6,000 = Rs. 14,000
Then list price=Rs. 14,000 and for this 10% discount is given.
10% of 14,000 = 10/100 × 14,000 = 1,400
Invoice price = 14,000 – 1,400 = Rs. 12,600

Question 7.
What is Banker’s discount?
Answer:
The interest on the face value of the bill from the date of discounting to the due date of the bill is known as Banker’s Discount.
Formula – B.D. = $$\frac{A n R}{100}$$ A = Amount, n = years, R = rate %

Question 8.
What is Bankers gain?
Answer:
The difference between the Bankers discount and the true discount is the banker’s gain.

Question 9.
What do you mean by present value of Bill.
Answer:
The actual selling price is called the present value of bill.
Or
The value of a debtor a date prior to its due date is called the present value of Bill.
p = $$\frac{F}{1+r n}$$

Question 10.
What is True Discount?
Answer:
Difference between the actual price and the sum due is called True Discount.
Or
True discount is the simple interest on the present worth or original sum due.
T = $$\frac{A n i}{1+n i}$$, n = no. of years, I = rate of interest

Question 11.
What is Bankers discount formula.
Answer:
B.D. = $$\frac{A n R}{100}$$ A = Amount, n = years, R = rate %

Question 12.
What is simple interest?
Answer:
It is the interest calculate for the principal amount for the time during which the money given is being used.

Question 13.
What is interest.
Answer:
Interest is the consideration which a borrower given to the lender for the money he has taken.

Question 14.
What is an amount.
Answer:
The total of principal and interest paid is called amount.

Question 15.
What is compound interest.
Answer:
Compound interest as the interest calculated on the principal and accrued interest.
Or
The interest produced after every fixed period is added to the principal for that amount we will again find the interest and the same procedure is continued till the stipulated time. This type of interest is called compound interest.

Question 16.
Write the formula for simple interest and compound interest.
Answer:
Here both principal and compound interest change from time to time
SI = $$\frac{P R n}{100}$$ P = principal, R = rate, n = \frac{P R n}{100}years
CI = A – P where A = P$$\left(1+\frac{R}{100}\right)^{n}$$

Question 17.
If simple interest on a certain sum is Rs. 360 for 2 years. @ 6% p.a. Find the sum.
Answer:
Given SI = 360 n = 2 years R = 6% P = ?
SI = $$\frac{P n R}{100}$$ P ∴ = $$\frac{S I \times 100}{\mathrm{n} \times \mathrm{R}}$$
= $$\frac{360 \times 100}{2 \times 6}$$ = 3000
∴ P = 3000

Question 18.
Find the compound interest on Rs. 2,560 for 3 years @ 8% p.a.
Answer:
CI = A – P Given p = 2560, n = 3, R = 8%
A = P$$\left(1+\frac{6}{100}\right)^{n}$$
= 2560$$\left(1+\frac{8}{100}\right)^{3}$$
= 2560 (1.08)3
A = 3224.86
CI = A – P
= 3224.86 – 2560
CI = 664.86

Question 19.
Find the simple interest on Rs: 2276 for 2 years 6 months @ 12.5% p.a.
Answer:
SI = $$\frac{P n R}{100}$$ P = 2276, R = 12.5%, n = 2.5 years (2 years 6 months)
SI = $$\frac{2276 \times 2.5 \times 12.5}{100}$$ = 711.24

Question 20.
Find the SI on Rs. 285 for 2 % years @3 percent. What is the amount after 2 % years.
Answer:
P =285, n = 2.5 years, R = 3%
SI = $$\frac{P R n}{100}=\frac{285 \times 2.5 \times 3}{100}$$ = 19.35
Amount A = P + SI = 285 + 19.35 = 304.35

Question 21.
Find the rate of interest for Rs. 200 to earn Rs. 80 interest for 5 years.
Answer:
Given p = 200, n=5.years SI = 80, R = ?
SI = $$\frac{P n R}{100}$$ R = $$\frac{S I \times 100}{P n}$$
= $$\frac{80 \times 100}{200 \times 5}$$ = 8
R = 8%

Question 22.
How much interest will be earned on Rs. 2,000/- @ 8.5% simple interest in 2 years.
Answer:
Simple interest SI = Pni = 2000 × 2 × $$\frac{8.5}{100}$$ = Rs. 340

Question 23.
What is an Annuity?
Answer:
An annuity is a fixed sum of money payable periodically at equal intervals of time under certain conditions.
The interval may be either a year or half year or a quarter year or a month. If interval is not mentioned then the time is taken as a year.
In other words, an annuity is a series of fixed amount of money paid at regular intervals of time.

Question 24.
What are different types of Annuities?
Answer:
Annuities may be broadly classified as follows-

1. Annuity certain
2. Annuity contingent
3. Perpetual annuity or perpetuity
4. Deferred annuity

Question 25.
What is the meaning of Annuity certain?
Answer:
When an annuity is payable unconditionally for a given length of time, it is called annuity certain or life annuity.

Question 26.
What is Annuity contingent?
Answer:
An annuity which is payable till the happening of an event is called annuity contingent.

Question 27.
What is the meaning perpetuity?
Answer:
If an annuity is to continue for ever, it is called annuity perpetual or perpetuity.

Question 28.
What is Deferred annuity?
Answer:
An annuity which is payable after a lapse of a number of intervals of time is called deferred annuity.

Question 29.
What is Annuity Immediate?
Answer:
If the payment on annuity is made at the end of each interval of time, the annuity is called immediate annuity.

Question 30.
What is Annuity due?
Answer:
If the payment is made at the beginning of each interval of time the annuity is called annuity due.

Question 31.
Give the commercial applications of annuities?
Answer:

1. Bank loans are taken for various purposes and loans are repayable in instalment are annuities
2. Lease rentals when assists are leased are annuities.
3. The premiums payable on life insurance policies are annuities.
4. The monthly deposit we make with banks are annuities.
5. Buying ofT.V. Fridge, car etc under instalment scheme the equated monthly instalments are annuities.
6. Interest received from the investments on debentures, government bonds etc. are the annuities.

Question 32.
What is the present value of annuity?
Answer:
The sum of the present values of all the payments is called the present value of annuity.

Question 33.
What is amount of Annuity?
Answer:
The sum of all instalments with interest due at the end of a given period is called the amount of annuity or accumulated sum of annuity.

Question 34.
What is the meaning sinking fund?
Answer:
A sinking fund is a fixed amount of money deposited periodically which grows with compound interest in order to meet some future liability. Eg.: Liquidation of loan or a debenture stock for replacing a machine or for meeting the education expenses.

Question 35.
What is Amortization?
Answer:
When loans are repaid in equal periodical instalments, each instalment amount is split up into two components called repayment of principal and payment of interest on the outstanding balance. The principal components in these instalments are called amortization.

Commercial Mathematics Short Answer Type Questions

Question 1.
What is more beneficial to the buyer if two companies A and B have the same list price of an article but x offers discounts of 20% and 15% and y offers discounts of 20%, 10% and 10%.
Answer:
Let the list price be Rs. 100
Case i : For the Company X,
Invoice price at 20%, discount=List price – Trade discount
= 100 – 20/100 × 100 = 100 – 20 = Rs. 80
Then Invoice price at 15% discount for Rs. 80 = 80 – 15/100 × 80
= 80 – 12 = Rs. 68
Case ii :(For the Company Y):
Invoice price at 20% discount for Rs. 100 = 100 – 20/100 × 100 = 100 – 20= Rs. 80
Invoice price at 10% discount for Rs. 80 = 80 – 10/100 × 80 = 80 – 8 = Rs. 72
Invoice price at 10% discount for Rs. 72 = 72 – 10/100 × 72 = 72 – 7.2 = Rs. 64.8
Therefore Company x is more beneficial to the buyer.

Question 2.
A person sells a shirt at Rs. 400. For every 24 shirts purchased on shirt is given free and his profit is 20%. Find the cost price.
Answer:
Let the list price be Rs. 100
Since the person realises the cost of 24 shirts by selling 25 shirts
Therefore selling price of each shirt = 400 × 24/25 = Rs. 384
Let x be the cost price
Then selling price = cost price + profit.
= x + 20x/100 = x + 0.2x = 1.2x
Then 1.2x = 384
Therefore x = 384/1.2 = Rs. 320
Therefore Cost price of each shirt = Rs. 320

Question 3.
A manufacturer sold goods to a retailer offering a trade discount of 15% off the list price and for cash payment, a further discount of 10% off the price is so reduced. If it gives a profit of 12% on the goods sold find how much percent the list price is higher than the cost price.
Answer:
Let the cost be Rs. 100
Add 12% profit on the cost = 100 + 12/100 × 10 = 100+ 12 = Rs. 112
Cash price=Rs. 112
Invoice price = Cash price + cost discount of 10%
= 112 + 112 × 10/90= 112 + 12.44 = 124.44
Add trade discount at 15% on list price = 124.44 + 15/85 × 124.44
= 124.44 + 21.96 = 146.40
Thus list price =Rs. 146.40
Then percentage increase of list price over cost price = 46.40/100 ×x 100 = Rs. 46.40%

Question 4.
Mrs. Sheela borrowed Rs. 30,000 for 6 years. Calculate compound interest @ 12% p.a.reckoned quarterly.
Answer:
Given: P = 30,000
t = 6 years
r = 12/4 = 3%
A = $$P\left(1+\frac{R}{100}\right)^{t}$$
= 3000$$\left(1+\frac{3}{100}\right)^{6 × 4}$$ (because reckoned quarterly)
= 30,000 (1.03)24
= 60981
∴ C.I. = A – P = 60981 – 30,000 = 30,981

Question 5.
In what period will Rs. 750 amount to Rs. 975 at 5% p.a. simple interest?
Answer:
Given = P = 750, A = 975, r = 5% t = ?
S.I. = A – P = 975 – 750 = Rs. 225/-
SI = $$\frac{P T R}{100}$$ ∴ T = $$\frac{S I \times 100}{P R}$$
= $$\frac{225 \times 100}{750 \times 5}$$ = 6
∴ Time T = 6 years

Question 6.
A men lost 5% by selling an article for Rs. 28.50 for how much he should sell to gain 10%?
Answer:
Let the cost price be Rs. 100
The SP is Rs. 95 (i.e., 100 – 5)
Similarly if SP is Rs. 28.50 what is Cp?
CP – SP
100 – 95
x = 28.5
∴ x = $$\frac{100 \times 28.50}{95}$$ = Rs.30
The cost price is Rs. 30
To gain 10% = 30 + 10% of 30 = 30 + $$\frac{10}{100}$$ × 30 = 33
He should sell at Rs. 33.

Question 7.
After allowing a discount of 7 1/2% on the marked price of an article, an article is sold for Rs.555. Find its marked price.
Answer:
Let the marked price be 100
Less Discount 7.5%
Selling price = 92.50
If SP. Is 92.5 maixed price = 100
If S.P. is 555 marked price = ?(x)
∴ x = $$\frac{100 \times 555}{92.5}$$ = 600

Question 8.
At that rate present CI p.a. will be Rs. 640 amount to Rs. 774.40 in 2 years.
Answer:
A = 774.40 p = 640 n = 2 years r = ?

r = 0.1 × 100
R = 10%

Question 9.
M. borrowed Rs. 12650 from a money lender a 18% p.a. simple interest. After 3 years, he paid 10381. He gave a buffalo to clear off the debt. What is the cost of buffalo?
Answer:
SI = $$\frac{P R n}{100}=\frac{12650 \times 3 \times 18}{100}$$ = 6831
Amount = SI + P = 6831 + 12650 = 19481
Amount = 19481
Cash paid = 10381 Difference = 9100
The cost of buffalo is Rs. 9100.

Question 10.
What is the face value of a bill discounted at 5% p.a. 73 days earlier than the date of maturity, the banker’s gain being Rs.10 only?
Answer:
B.G = T.D. × n × $$\frac{r}{100}$$
10 = T.D. × $$\frac{73}{365} \times \frac{5}{100}$$
T.D. = Rs.1,000 BD = T.D. + B.G = 1,000 + 10 = 1010
Face Value BD $$\frac{B D \times T D}{B G}=\frac{1000 \times 1010}{10}$$ Rs.1,01,000.

Question 11.
If the bankers gain on certain bill due 6 months is Rs. 10 & the rate of interest 10% p.a. Find the face value of the bill.
Answer:

0.05A = 1.05(0.05A – 10)
0.05A = 0.0525A – 10.5
0.5A – 0.525A = 10.5
-0.0025A = -10.5 A = $$\frac{-10.5}{-0.025}$$
A = 4200 ∴ Face value of the bill = 4200/-

Question 12.
Find the difference between the S.I. and C.I. on Rs. 3,000 in 3 years at 4% p.a.
Answer:
Given P = 3000 n = 3 r = 4%
SI -= $$\frac{p n r}{100}=\frac{3000 \times 3 \times 4}{100}$$
S.I. = Rs. 360
C.I. = A – P
A = $$P\left(1+\frac{r}{100}\right)^{n}$$
= 3000$$\left(1+\frac{4}{100}\right)^{3}$$
= 3000 (1.04)3
= 3000 × 1.124
A = 3374.592
C.I. = A – P
C.I. = 3374.592 – 3000
= 374.592
Difference between the S.I. & C.I. is 374.592 – 360 = 14.592

Question 13.
A Banker discount bill which has to run 73 days before it is legally due at 6% p.a. & bankers gain is Rs. 60 for what sum the bill was drawn?
Answer:
R = 7%p.a. or for $$\frac{1}{5}$$ years. It is $$\frac{1}{5}$$ × 6 = $$\frac{6}{5}$$% = 1.2%
BG = SI or TD
TD = B.G. × $$\frac{100}{R}$$ = 60 × $$\frac{100}{1.2}$$ = 5000
∴ TD = 5000
BD = TD + BG
= 5000 + 60 = 5060
Bill Value = BD × $$\frac{100}{R}$$ = 5060 × $$\frac{100}{1.2}$$
Bill Value = Rs. 4,21,666.

Question 14.
Raju borrowed Rs. 62,500 and paid Rs.67,600 in full settlement after 2 years. Find out the rate of compound interest.
Answer:
Given, P = Rs. 62,500, A = Rs. 67,600,T = 2years
C.I. = A – P = 67,600 – 62,500 = Rs. 5,100

R = 0.04 × 100 R = 4%

Question 15.
A company’s yearly profits are found to have risen in the ratio 12 : 13 if in the previous year. The profits were Rs. 13,800. Find the profits this year?
Answer:
Let the profits in the previous year be 12x
And profits in the present year be 13x where x is the unit charge.
It is given that previous year profits = 13800
∴ 12x = 13800
x = $$\frac{13800}{12}$$x = 1150
Hence the present year profit= 13x
= 13 × 1150
= Rs. 14,950
The profit this year = Rs. 14,950.

Question 16.
What would be the amount of Compound interest (CI) on Rs 5,000/- at 5% rate of interest p.a. for 3 years?
Answer:
Compound interest CI = A – P = P(1 + i)n – P = P[(1 + i)n – 1]
Where P = 5000, i = $$\frac{5}{100}$$ = 0.05, n = 3 yrs.
∴ CI = 5000 [(1.05)3 – 1] = 5000 [1.1576 – 1] = 5000[0.1576]
= Rs. 788.13

Question 17.
Find :
i) TD,
ii) BD,
iii) BG on a bill of Rs. 10,450 due 3 months hence @5% p.a.
Answer:
Here Face value of the bill A= Rs. 10,450, n = $$\frac{3}{12}$$ years, i = $$\frac{5}{100}$$ = 0.05
∴ ni = $$\frac{3}{12}$$ × 0.05 = 0.0125
i) TD = $$\frac{\text { Ani }}{1+n i}=\frac{10450 \times 0.0125}{1.0125}$$ = 129.012 ie Rs. 129.01
ii) BD = Ani = 10450 × 0.0125 = 130.625 ie Rs. 130.63
iii) BG = BD – TD = 130.63 – 129.01 = Rs. 1.62

Question 18.
Find the amount of annuity if payment of Rs. 300 is made at the end of each year for 4 years at the rate of 10% p.a. compounded yearly.
Answer:
A = ?, P = 300, n = 4 yrs. i = $$\frac{10}{100}$$ = 0.1
Amount of annuity is
Amount of anuity = A = $$\frac{P}{i}$$[(1 + i)n – 1]
= $$\frac{300}{0.1}$$ [(1.1)4 – 1] = 3000 [1.34431 – 1 ]
= 3000 [0.34431]
= Rs. 1032.93

Question 19.
A lady invested a total sum of Rs. 9,500 in two difference Banks which give 5% and 7% % simple interest. If both the amounts are going to be equal in 7 years. Find the individual investment.
Answer:
Total sum = 9500 Here i1, = 5% = $$\frac{5}{100}$$ = 0.05, i2 = 7 1/2% = \frac{7.5}{100}$$\frac{7.5}{100}$$ = 0.075
Let the money invested in 5% simple interest = Rs. X
Then the money invested in 7 % will be (9500 – x)
Then Amount A; =principal + simple interest
A1 = P1 + P1ni1
= x + (x × 7 × 0.05) = x + 0.35x = 1.35x
A2 = P2 + P2nI2
A2 = (9500 – x) + (9500 – x) 7(0.075)
A2 = 9500 – x + (9500 – x) 0.525
A2 = 9500 – x + 4987.5 – 0.525x
A2 = 14487.5 – 1.525x
After 7 years A1 = A2
i.e. 1.35x = 14487.5 – 1.525x
1.35x + 1.525x = 14487.5
2.875x = 14487.5
x = $$\frac{14487.5}{1.825}$$ = 7938.36
∴ The sum invested at 5% = x = Rs. 7938.36
The sum invested at 71/2% = (9500 – x) = 9500 – 7938.36
= Rs. 1561.64

Commercial Mathematics Long Answer Type Questions

Question 1.
A bill for Rs. 8,500 drawn on 25th April for 5 months was discounted on 17th July @ 5 p.a. Find the discounted value of the bill.
Answer:
Due date is 25th April + 5 months +3 days grace
28th September.
No. of days from 17th July to 28th Sep. is
July = 14 days (excluding first day)
Aug = 31 days
Sep = 28 days
∴ N = 73 days
Discounted value of the bill = F.V – B.D.
ie. = 3500 – $$\frac{A N R}{100}$$
= 8909 – $$\left[\frac{8500 \times \frac{73}{365} \times 5}{100}\right]$$
= 8500 – 85
= 8,415.

Question 2.
The bankers gain on a bill due in 4 months discounted at 15% p.a is Rs. 360. Find
(i) True discount
(ii) Bankers discount
(iii) Face value of the bill.
Answer:
(i) True discount TD = $$\frac{\text { B.G. } \times 100}{\mathrm{NR}}$$
TD = $$\frac{360 \times 100}{\frac{4}{12} \times 15}=7200$$ TD = 7200
(ii) Banker Discount
BD = BD + TD
= 3600 + 7200 = 7560
(iii) Face value of the bill
FV = $$\frac{100 \times \mathrm{BD}}{\mathrm{NR}}=\frac{100 \times 7560}{\frac{4}{12} \times 15}$$ = 1 51

Question 3.
A men left Rs. 1,30,000 for two sons aged 10 years and 16 years with the direction that the sum should be divided in such a way that the two sons get the same amount when they attain the age of 18 years. Assuming the rate of simple interest is 12 and half % p.a. Calculate how much the elder son got in the beginning.
Answer:
Let the share of the son aged 10 be x
Share of the son aged 16 = 1,30,000 – x
Date of maturity=each son is 18 years old.
Interval between maturity and present age 18 – 10 = 8 years
18 – 16 = 2 years
Amount of the son aged 10 = P + S.I. = x + $$\left(\frac{x \times 12.5 \times 8}{100}\right)$$
= x + x = 2x
Amount of the son aged 16 = P + S.I.
= (1,30,000 – x) + [1,30,000 – x) × $$\frac{12.5}{100}$$ × 2]
= (1,30.000 – x) + ((1,30,000 × X) × 0.25]
= 1,30,000 – x + 32500 – 0.25 x
= 162500 – 1.25x
∴ Rs. x are invested for 8 years and Rs. (1,30,000 -x) for 2 years and the respective amount are equal.
∴ 2x = 162500 – 1.25%
i.e., 162500 = 2x + 1.25x
3.25x = 162500
x = $$\frac{162500}{3.25}$$
x = 50,000
∴ the elder son share = 1,30,000 – x
1,30,000 – 50,000
= Rs. 80,000

Question 4.
A sum of money lent out at SI amount to Rs. 3224 in 2 years & Rs. 4160 in 5 years. Find the sum of the rate of interest.
Answer:
Amount is 5 years = 4160
Amount in 2 years = 3224
Difference = 936 = interest for 3 years
∴ Interest for 1 year = $$\frac{936}{3}$$ = 312
For 2 years interest = 624
Principal =Amount – Interest
= 3324 – 624
= 2600
∴ R = $$\frac{100 \times \mathrm{SI}}{\mathrm{pn}}=\frac{100 \times 624}{2600 \times 2}$$ = 12%

Question 5.
On a bill of Rs. 20,750 due after 8 months at 6% p.a. Find
(i) Present value
(ii) True discount,
(iii) Bankers discount,
(iv) Bankers gain.
Answer:

Question 6.
A sum of money amounts to Rs. 855 in 3 years at the rate of 4% p.a. simple interest. Find the sum.
Answer:
A = 855, n = 3.5 years, R = 4%, p = ?
SI = $$\frac{p n r}{100}$$ but SI = A – P
A – P = $$\frac{p n r}{100}$$A = P+ $$\frac{p n r}{100}$$
855 = P + $$\frac{p(3.5 \times 4)}{100}$$
855 = $$\frac{100 P+14 P}{100}$$
85500 = 100P + 14P
85500 = 114P
P = $$\frac{85500}{114}$$ = 750
∴ Principal = Rs. 750

Question 7.
The simple interest on a certain sum of money for 2 years is Rs.1,550 and the compound interest is Rs.1,588.75. Find the sum and the rate of interest.
Answer:
Let x be the principal
r = $$\frac{R}{100}$$ rate of interest
SI = 2x r = 1550 ……(1).
CI = x [(1 + r)2 – 1] = 1588.75 ….. (2)
Divde eqn 1 by eqn 2

r2 + 2r = 2.05 r
r2 – 2.05 r + 2 = 0
r2 – 0.05 r = 0
r(r – 0.05) = 0
r = 0 or r – 0.05 = 0 r = 0.05 ⇒ R = 5%
x = $$\frac{1550}{2 r}=\frac{1550}{2(0.05)}=\frac{1550}{0.1} x$$ = 15500
x – Principal – Rs. 15,500/- or R = 5%

Question 8.
A banker paid Rs.5,454 for a bill of Rs.5,500 drawn on 21st May due 6 months later. If the rate of interest is 6.1p.a. Find the date on which the bill was discounted.
Answer:

 Day Month Date of Bill 21 05 Bill period 00 06 Naminal due date 21 11 Grace period 03 00

∴ Legal due date24-11
∴ Total days will be
Nov. – 24 days
Oct. – 30 days
– 50 days
The bill was discounted on 5th October
Discounted value = Rs. 5,454
Face value = Rs. 5,500 – A
R = 6.1 % Bill period = 6 months
B.D. = face value – discounted value
= 5,500 – 5954 – 46 Rs.

∴ N= (0.1371 × 365) days
N = 50 days

Question 9.
A man invested a total of Rs. 9500 in two different banks which give 5% and 77% simple interest. If both the amounts are going to be equal in 7 years find the individual investment.
Answer:
Let the two investments be x and y.
x + y = 9500 ——– (1)
No.: of years = 7, Rate at 1st Bank = 5%.
Rate at 2nd Bank = 7%2%.
Amount = P + Si
Amount in 1st Bank x + $$\frac{x \times 5 \times 7}{100}=\frac{100 x+35 x}{100}=\frac{135 x}{100}$$
Amount in 1st Bank y + $$\frac{y \times 7.57}{100}=\frac{100 y+52.5 y}{100}=\frac{152.5 \dot{y}}{100}$$
Since both amounts are equal
$$\frac{135 x}{100}=\frac{152.5 y}{100}$$
135x = 152.5y ——– (2)
Solving (1) and (2) we get
y = 9500 – y ……. (3)
Substitute eqn. 3 in eqn 2
135 (9500 – y) = 152.5y
1282500 – 135y = 152.5 y
1282500 = 152.5y + 135y
∴ y =$$\frac{1282500}{287.5}$$
y = 4460.869
x = 9500 – y
x = 9500 – 4460.9
x = 5039.1

Question 10.
A sum of money invested at C.I. amount to Rs. 2916 at the end of 2 years and to Rs. 3149.28 at the end of 3 years. Find the sum and rate of interest.
Answer:
Formula: A = $$P\left(1+\frac{R}{100}\right)^{n}$$
At the end of 2 year
2016 = $$P\left(1+\frac{R}{100}\right)^{2}$$ ——— (1)
At the end 3 year
3149.28 = $$P\left(1+\frac{R}{100}\right)^{3}$$ ——-(2)
Divide (2) by (1) we get

Question 11.
A bill for Rs. 14,600 drawn at 3 months was discounted on November 11th for Rs. 14,544. If the role of simple interest is 4% p.a., on what date was the bill drawn?
Answer:
Face value of the bill = A = 14600
Date of discount = November 11th
BD = Banker’s Discount = 14600 – 14544 = 56
i = $$\frac{4}{100}$$ = 0.04
BD = Ani
1 + ni 56 = 14600 × n × 0.04
$$\frac{56 \text { years }}{14600 \times 0.04}$$ = n ie n = $$\frac{56 \times 365}{14600 \times 0.04}$$ = 35 days
ie. No. of days from November 11th to due date = 35 days
No. of days from date of drawing to November 11th
= 90 – 35 = 55 days
Date of drawing = 55 days before Nov. 11th = 11 days (November) +31 days (October) + 13 days (September) = 16th September

Question 12.
The difference between Banker’s discount and true discount on a bill due after 6 months at 4% p.a. interest being Rs. 20. Find
1) True discount
2) Banker’s discount
3) Present value
4) Face value of Bill
Answer:

ie Face value of the bill = A = Rs. 51,000
Banker’s discount = BD = Ani = 51,000 × 0.2 = 1,020
True discount = TD = $$\frac{A n i}{1+n i}=\frac{1020}{1.02}$$ = 1000
Present value = A – TD= 51,000 – 1,000 = 50,00

## Banker and Customer Relationship Long Answer Type Questions

Question 1.
Explain relationship between the Banker and Customers.
Answer:
The relationship between banker and customer depends on type of services offered by the banker to customer. The banking business depends on the good faith and mutual understanding between customer and banker.
Relationship between banker and customers may be divided into two types
1) General relationship
2) Special relatioship
1) General relationship :
The general relation of banker and customer includes
a) Relationship as debtor and creditor
b) Relationship as bailor and bailee
c) Relationship as trustee and beneficiary
d) Relationship as agent and principal

a) Debtor and creditor relationship:
Debtor and creditor relationship between banker and customer is called as primary relationship. Banker receives money from customer in the form of deposits therefore banker is called as a dignified debtor Banker the debtor for his customer and bound to discharge his indebtedness by honoring his customer’s cheques. Customer is called as insecured creditor because he cannot exercise any claim over the assets of banker. But customer has the right to demand back his money and the banker is under obligation to repay the debt as and when he is required to close.

b) Bailor and bailee relationship :
Customer can keep securities and valuables in the bank for safe custody. In these cases banker is called as bailee and customer is bailor. Banker as a bailee, should protect the valuables in his custody with reasonable case. In case of loss due to
negligeney of hacker in protecting valuables banker is liable to pay such loss.

c) Agent and principle relationship :
Banks provide certain agency services to ifs customer. Agency services includes buying and selling of securties collection of cheques , bills drafts, divides and payment of bills, preminium etc… In these cases banker and customer relationship is in the form of an agent and principal

d) Trustee and beneficiary relationship :
Banker acts as a trustee for managing the assets of customers. In this type of relationship trust fund or asset should be managed by banker in accordance with the trust agreement and profits earned by trust transactions should be credited to beneficiaries account.

2) Special relationship between banker and customer :
It includes
a) Obligation to honour cheques.
b) Obligation to maintain the secrecy of accounts
c) Right of general lien
d) Right of set-off
e) Garnishee order
f) Right of appropriation
g) Right to charge compound interest and incidental charges
h) Law of limitation.

a) Obligation to honour cheques :
Banker is bound to honour his customer’s cheque provided when customers present the cheque for repayment of deposit, it is the duty of the bankers obligations to honour his pay the money but the bankers obligations to honour his customers cheques is subject to the fulfillment of certain conditions. They are

• Availability of sufficient funds in customer’s account
• Funds must be properly applicable to the payment of cheque
• Banker’s required to pay the amount to the customer if it is correct in all respects
• Cheques should be presented within reasonable time for payment.
• Customer’s cheque should be free from legal restrictions on payment of cheque.

b) Obligation to maintain the secrecy of accounts :
Banker’s obligation is to keep the transactions of his customers in secret except under special circumstances. Banker can disclose the customers account to outsides in the following circumstances.

• Where there is an expressed consent of the customers
• Where there is an implied consent of the customer.
• Where disclosure is under compulsion of law
• Where there is duty to the public to disclose
• Where the intrest of the banks requires disclosure
• Where the information is required by another banker.

c) Right of general lein :
General lein is a special right of the banker to retain all the propecties of his customers till all the same due to the bank are recovered. The main object of this is to have protection for the funds. General lien provides the eight to the banker to sell the securities of the customer when customer fails to clear the debt as per schedule.

d) Right to set off :
It is the right of the banker to adjust an amount due to him from the customer as against the amount payable to the customer. It is a legal right which helps the banker to combine all the accounts in the name of same customer to adjust debit balance in accounts with the credit balance in another account. This right of the banker ensures the safety of funds. Banker should make an agreement with the customer authorizing him to combine the accounts without notice.

e) Garnishee order :
The obligation of a banker to his customer’s cheque is extinguished on receipt of an order of the court known as the garnishee order. If a person failed to repay his debt to his creditor, the creditor can apply to court for issue of garnishee order which suspends the operation of debtors account.

f) A Right of appropriation : .
When a customer owes several distinct debt the question of appropriation case. The payment made by the customer may not be sufficient to clear all debts due by the customer similarly when a customer holds more than one current account and regularly operates these accounts by depositing funds and making with drawals simultaneously in all accounts he holds, banker has to follow the rules governing the appropriation.

g) Right to charge compound interest and incidental charges :
Banker has right to charge interest on advances and a reasonable incidental charges for other services rendered by him. It is an implied right available to a banker. Standard rates are fixed and made known to customer incase of commission for services like collection of cheque bills etc.

h) Law of limitation :
Generally debts become time barred after three years from the due date. As per the law of limitation a creditor forgoes the right to recover the amount from a debtor after the expiry of the period of limitations. According to the Indian limitation act of 1963 debt becomes time barred if it is not repaid within 3 years from the date of contractor due. It means that the creditor cannot take any legal action against the debtor for the recovery of amount due from the debtor after the expiry of 3 years from the date of due or contract.

Question 2.
Comment on the banker’s obligations to maintain secrecy of his customer’s account.
Answer:
It is a general understanding between the customers and the banker that the bankers should maintain secrecy regarding the customers account it is believed and the facts that if the account are disclosed to others the image of the customer will be lost or it would damage the customers position and prestige. Hence it was the practice of the banker not to disclose the amounts and banking operations of the customers to others and this was legalized.

It is one of the implied terms of contract between banker and customer is that banker is obliged to keep the affairs of his customer secret except under special circumstances. Maintenance of secrecy is not only regarding the debit and credit balance of the amount · but also to all the transactions that go through the amount and to the securities if given in respect of the account. This obligation continues even after the amount is closed and extends after the customer’s death also.
The following circumstances under which the banker can disclosed the state of affairs of the customers-

a) Disclosure under compulsion of law :
The banker can disclose the accounts of the customer as and when demanded by the authorities as per the law. Before disclosing the information banker should carefully information should be confined to the point asked only.

b) Disclosure at public interest :
If a customer holds an illegal account which is against the interest of the nation the bankers should disclose the account to proper authority. Under following circumstances bankers can disclose information to public.

• Where the bank consider that customer is involved in activities prejudicial to the interest of the country.
• Where the banks reveal that the customer’s is contravening the provisions of any. law.
• Where sizeable funds are received from foreign countries by a constituent.
• Where the information in the bank’s possession may lead to the apprehension of the culprit.
• Where the citizen of a nation has trade links with an enemy country or during war.

c) Disclosure with the consent of customer :
The banker can disclose the state of affairs of the customers account when the customer gives his consent to disclose the account. The consent may be expressed or implied. A customer may authorized his agent to collect information.

d) Disclosure in the interest of bank :
The banker is his own interest can disclose the account of the customer. The banker is justified in disclosing information to a generator of the account.

e) Disclosure as common courtesy :
If a fellow banker asks about the credit worthiness of a customer. The banker is obliged to disclose by answering credit enquires.

Question 3.
Explain the various subsidiary services of a modern banker (Agency Services).
Answer:
The important general utility services of Banker are-
a) Safe custody :
A Banker accepts precious jewels, life insurance policies, title deeds to property Government securities, shares and debentures for safe custody. A Banker accepts and ensures safe custody of valuables of its customers.

b) Dealing in Foreign exchange business :
Commercial Banks also offer a number of services in respect of Foreign Exchange Business. It includes –

• Export finance : Banks also grant export finance to exporters. They provide pre shipment advance, post shipment advance a concessional rate of interest.
• Import Credit: Banks also help the importers to importgoods on credit by granting them commercial letter of credit.
• It also help the importers by realizing the imported goods against trust receipts signed by the importers.
• It also execute deferred payment guarantee on behalf of customers.
• It also issue solvency certificates, letter of introduction etc.
• It also collect trade information about foreign markets and also pass on such information to importers and exporters.

c) Issuing of Travellers letters of credit, circular notes and travelers cheques : . A Banker also issues travellers letter of credit,circular notes and travellers cheques to the tourists.

d) Acting as a reference :
A Banker acts as reference regarding the financial standing of his customers, by serving as a referee. The banker enables his customer to enter into business relations with other businessmen.

e) Collecting information about businessmen for customers :
A Banker collects information about other businessmen through their fellow banker and supplies that information to his customers.

f) Collection of statistics and data :
Banker collects statistics and data about banking, commerce, industry, agriculture, foreign trade etc., and publishes them in it periodicals or magazines.

g) Collection’of money on behalf of customers :
Banker collects crossed and uncrossed cheques and Bank Drafts on behalf of the customers. He also collects bills of exchange and promissory notes on behalf of the customers. He also collects postal orders for the customers and interest and dividends on the cupons.

h) Collection and payment of pension :
A Banker also perform another agency services i.e. collection and payment of pension. This services is rendered by most of the Nationalised Banks in India.

i) Making of payment on behalf of customers :
A Banker undertakes to make payments on behalf of his customers. He pays the bills . of exchange and promissory notes life insurance premium, subscriptions to clubs, subscriptions to newspapers, rents to land lord etc., on behalf of customers. After making the payments on behalf of the customers, the banker is required to bring the same to the notice of the customers.

j) Purchase and sale of securities on behalf of customers :
The Banker undertakes to buy and sell securities on behalf of a customers. The Banker arranges for the purchase the sales of securities through stock brokers.

k) Advising customers regarding stock exchange investment :
Banker collects information on various stock exchange securities and advises the customers on the basis of the information collected.

l) Arranging for remittance of funds on behalf of customers :
A Banker arranges for remittance of funds from one place to another on behalf of thief customers by means of bank drafts, mail transfers and telegraphic transfers.

Question 4.
Explain the special relationship between banker and customer.
Answer:
The special relationship between banker and customer are -Special relationship means the mutual obligations and rights of the banker and the customer arising out of their general debtor and creditor relationship.
The relationship are-
1) Banker’s obligations,
2) Bankers rights,
3) Bankers obligations coupled with his rights or banker rights coupled with obligations.

1) A) Bankers obligations to honours his customers cheque
The banker’s primary contract is to repay the money received for his customer’s account usually by honouring his cheques. But there are certain conditions –

• Sufficient funds must be available in customer’s account.
• Bankers obligations to honour cheques extends even cheques drawn against overdraft.
• Banker’s obligations to honour cheques doesnot apply to cheques drawn against uncleared cheques or bills.
• Funds must be properly applicable to the payment of cheque.
• Bankers must be duly required to pay cheque.
• There must be no legal bar preventing the payment of cheque.

B) Bankers obligations to mention the secrecy of the customers account A banker should not disclose the state of the customers account to any outsider. But there are certain exceptions to observe secrecy.

• When there is an express consent of customers.
• When there is an implied consent of customers.
• When he is compelled by laws of country.
• When he is under a public duty to disclose.
• When its own interest requires disclosure.
• When an enquiry secured from a fellow bankers.

2) Bankers Rights : The various rights of banker are –

• Banker right of general lien : Lien is the right of a banker to retain the property in his possession, belonging to another until the debt due from the owner of that property is repaid.
Lien is of two types general and particular lien.
Particular lien is rights of creditor to retain particular property.
General lien is right of creditor to retain any property until the general balance is repaid.
• Bankers right to set off or bankers right to combine accounts: A bankers right to set-off refers to the right of a bankers to combine or adjust the debit and credit balances of two or more similar accounts held by customers in the same capacity.
• Bankers right to charge compound interest.
• Bankers right to charge incidental charges.
• Bankers right to levy commitment charges.
• Bankers right not to produce books of accounts under banker’s books evidence act of 1891.

3) Bankers obligations coupled with his rights or bankers right coupled with his obligations : There are certain cases in which a banker ahs obligations coupled with his rights coupled with his obligations such cases are –

• Banker’s rights and obligations regarding appropriation of payments as per this rights when a customer owes several distinct debts to a banker and makers a payment which is insufficient to discharge all the debts simultaneously a questions arises as to which debt the payment should be appropriated. These type of situations should be tackled in accordance with the rules governing the appropriation of payments.
• Bankers obligations and rights when a customer’s account is attached by a garnishee order as per garnishee order banker can set off or combine all the accounts of his customer kept in the same capacity or right in all the branches of bank and banker has right not to retain any funds of the customer for meeting the customer’s future or contingent debts.

Question 5.
What are precautions a banker should take in dealing with the Joint Account Holders?
Answer:
The following precautions were taken by a banker while opening the joint account.

• The banker has to ensure that the joint account is opened in the names of only adultmembers competent to enter into contracts.
• He should also see the joint account is signed by all the persons interested to the joint account.
• He should ascertain the style or title under which the joint account is to be opened.
• The banker should bear in mind that the joint account holder can delegate the authority to operate the joint account to any of them or even to an outsider.
• The banker should also get clear instructions as to how the credit balance in the joint account is to be disposed off in the event of the death of any of the joint account holder.
• The banker receives a notice of the revocation of authority from any joint account holder, he should act accordingly and stop the operations on the joint account.
• The banker should get clear instructions in writing, signed by all the joint account holders, whether the person or persons who are authorised to operate the joint account are also given the power to overdraw or take any other advance on the joint account.
• The banker should not permit him to withdraw securities or safe deposits unless he is given specific authority to do so.
• The notice of the insolvency of any one of the joint account holders, the banker should stop the operations on the joint account.
• The notice of the insanity of any one of the joint account holders, it is advisable for the banker to stop the operations on the joint account.

Question 6.
What are the precautions a banker has to take while opening and operating?
a) Executors and administrators account.
b) Partnership firm accounts.
Answer:
a) Executors and administrators account : The bank should observe the following legal aspects in opening and operating the accounts of executors or administrators.

• The banker should stop the operation of the testator’s account, when he receives the message of the death of testator.
• A copy of the letter of probate should be field for future reference.
• The banker should collect the “Letter of Administration’ to ascertain whether he is the : person to execute the property of the deceased.
• The account of the deceased should be closed and transfer the funds to the newly opened account of administrator or executor.
• If two or more executors or administrators are appointed, the banker should follow all the rules and regulations as followed in the case of joint accounts.
• The banker should not transfer any funds to the personal accounts of the executors.
• The borrowings made by the executor to meet the expenses of the deceased estate or for clearing the debts of the deceased shall however be in his personal capacity.
• The executor can overdraw or borrow in his personal capacity and cannot make liable the property of deceased for such borrowing.

b) Partnership firm accounts :
There are many precautions to be followed while opening the account in the name of partnership firm.

• A Banker can open a partnership account when one or more partners apply to him to do so, after satisfying himself, either from an examination of the partnership deed, or from proper enquires, that the partner or partners are entitled to do so.
• A Banker should not open a firms account in the name of a partner or partners. He should open in the name of the firm.
• He should obtain a copy of the partnership deed.
• If there is no partnership deed, it is advisable for the banker to obtain a letter called the “partnership” letter signed by all the partners.
• It is better for the banker to obtain a mandate signed by all the partners stating the name or names of the partner or partners who are authorized to operate the firms account.
• It is advisable for the banker to get clear instructions about the powers given to the partner or partners who are authorized to operate the firms account.
• The banker should obtain the specimen signatures of the authorized partner or partners and he should get the specimen signatures of all the partners of the firms.
• He should also honour only those cheques drawn in the firm’s name and signed by the ” authorized partner or partners.
• He should bear in mind that the authority given to the authroized partner or partners to issue cheques can be cancelled by any of the partners.
• He should see that the funds of the firms do not go to the personal account of any partner.
• Before granting any advance to a firm, he should satisfy himself as to the credit worthiness of the firm by examining its balance sheets for the preceding two or three years.
• When a loan granted to a firm, it is in the interest of the banker to obtain an undertaking from all the partners to repay the advance jointly or severally.
• When a banker accepts the guarantee of a firm, he should ensure that the guarantee is executed by all partners of the firm.
• On the admission of a new partner to the partnership firm, the banker should close the account of the firm and open a new account in the name of the reconstituted firm, if the firm’s account shows a debt balance.
• The notice of the retirement of a partner, the banker should not honour the cheques drawn by the retired partner unless they are confirmed by the remaining partraurs.
• In case of the notice of the death of a partner, the banker should not honour the cheques drawn by the deceased partner without getting the confirmation of the remaining partners.

Question 7.
What precautions to be taken by banker while opening and operating an account in the name of minor?
Answer:
Under Section 3 of Indian Majority act 1875 a minor is a person who has not completed the age of 18 years according to contract act 1872 minor is incompetent to enter into contract therefore contract with minor person is viod. But minor can issue cheques and a banker can open saving account or current account in the name of minor and allow him to operate it. Banker has no risk as long as minor’s account is in credit. Banker should be very careful in opening and maintaining an account with a minor following precautions should be taken by the banker,

• It is better to open saving bank account in the name of minor and not the current account.
• Banker is advised to open a minor’s account in the name of his natural or legal guardian.
• When a minor is appointed as an agent to operate the bank account of another person banker should obtain a written authorization from the principal appointing the minor as his agent and specified the various powers given to the minor agents.
• When a minor is admitted to the benefits of a partnership firm he will not liable for the debts incurred by the firm during his minority therefore banker should be very careful in lending to a partnership firm in which there is a minor partner.
• When a joint account is opened in the name of minor and adult, minor cannot be made liable for any overdraft or loan given to that joint account.
• Banker should not accept the guarantee of minor for a debt due from a principal debtor.
• Minor cannot be appointed as a trusee and banker should not permit a minor to operate a trust account.
• A minor may be appointed as an executor but it is advisable for a banker not to permit a minor to operate a bank account as an executor.

Question 8.
What are the precautions to be taken by banker while opening the account in the name of joint stock company.
Answer:
Joint stock company is an association of persons registered under the companies act 1956. It is a legal artifical person created by law. There bank account can be opened in company’s name.
While opening and maintaining an account in the name of joint stock company a banker is required to take the following precautions.

• Banker should examine the original certificate in corporation to ascertain whether the company is legally incorporated or not banker should obtain a certificate copy of the in corporation certificate for his reference.
• Banker should inspect the original business commencement certificate to ascertain whether the company is authorized to commence business banker should also obtain certified copy of the business commencement certificate for his reference.
• Banker should obtain a certified copy of memorandum of association of the company to know about authorized capital liability of share holder object of the company etc.
• Banker should get a certified copy of the articles of association of the company to find out the powers of direction to draw and endorse cheque to accept bill of exchange to borrow money etc.
• Banker should obtain a list of the directors of the company signed by chairman.
• Banker should collect the copy of the resolution of the board of directors certified. by chairman to open an account in the name of company with the bank along with application for opening an account.
• Banker should collect the copy of resolution to know about the names of directors and officers of the company who are authorized to operate the account.
• Banker should obtain the specimen signatures of the persons who are authorized to operate company’s account.
• In case of existing company banker should collect satest banlance sheet audited by qualified auditor to ascertain the financial postion of the company.

Banker should observe certain formalities to grant loan to a company they are

• Banker should satisfy himself that the company has power to borrow.
• Banker should obtain resolution copy of the board of directors of the company to borrow loans from bank.
• Banker should compare the borrowing amount with paid up capital of the company because borrowing amount does not exceed its paid up capital and reserves.
• Banker should ensure that the company borrows only for the purpose mentioned in the memorandum of association.
• Banker should sanction loan to a company against some of its assets which are free from other changes.
• Banker should stop the operations on the company account on the receipt of the notice of the liquidations of the company.

Question 9.
Explain the different types of NRI account.
Answer:
Non resident Indian is an Indian citizen who stays abroad for employment or carrying on his business outside India or stays abroad under circumstances indicating an intention for an uncertain duration of stay abroad.
NRIs are granted the following facilities
a) NRIs can maintain bank account in India.
b) NRIs can invest in securities and shares of Indian companies.
c) NRIs can invest money on immovable property in India.
d) NRI can maintain current account, savings account, term account, rupee account with authorized banks in India.
e) NRI can maintain accounts in Indian currency as well as in foreign currency.
1) Rupee account (Indian currency account):
NRI can open Rupee account in following manner.

• Non-Resident Rupee ordinary account:
This account may be in the form of current, savings or term deposit account. The amount credited to this account cannot be remitted outside India.
• Non-Resident (external) account :
The deposit account maybe current account, savings account’or fixed deposit account Deposit amount is held in Indian rupee amount from amount can be remitted outside India at the current exchange rate.
• Non-Resident rupee deposit amount :
This type of account is in the form of fixed deposit for a period of 1 to 3 years, the deposit would be in Indian rupee. Intrest earned on this deposit may be repatriated outside India at the current exchange rate.
• Non resident rupee account :
This account maybe current account, savings account, fixed deposit account, requiring deposit account. Deposit amount would be accepted in Indian rupee only.

2) Foreign currency account :
Only fixed deposits are accepted under the scheme for a period not less than one year and not more than 3 years. Deposit amount is accepted in fire different currencies US dollars, Pound, yen, Deutsche, Mark, Euro.

Question 10.
Explain the general relationship between banker and a customer.
Answer:
The general relationship between banker and a customer are as follows:
Relationship of Debtor and Creditor: Banker accepts deposits of money from his customers for the purpose of lending and investment and repays it on demand as per the terms of the contract of deposit. In fact, deposit accepted by the bank is technically money loaned out to the bank from the depositors. Therefore, the general relationship between a depositor and the banker is a relation of the debtor and the creditor. The depositors are creditors and the bank is the debtor. However, the relationship between the banker and customer is directly opposite when the bank lends money to its customer. The bank becomes the creditar and the customer becomes the debtor.

Relationship of Trustee and Beneficiary: Wiian a banker accepts items like securities or documents for safe custody or maintains escrow accounts of the customers, the relation between the banker and customer is a Trustee and the beneficiary (Trustier). The bank is the Trustee and the customer is the beneficiary.

Relationship of Lessor and Lessee: Similarly, when a customer hires a safe deposit locker from the bank, the relation between the bank and the customer is lessor and lessee. The bank is the lessor (licensor) and the hirer of safe deposit locker is the lessee (licensee/tenant).

Relationship of Principal and Agent:When a bank collects cheques, bills and other instruments for customers, the relation between the bank and customer is that of Principal and Agent. The bank also makes regular payments of insurance premium rent étc. as per standing instruction received from the customer. In the above cases also the relation between the bank and the customer is of Principal and agent. The bank act as the agent and customer the principal.

Relationship of Assigner and Assignee: An assignor is a person who transfers his security rights to a lender as collateral to the money borrowed by him. The transfer of Life Insurance Policies, National Saving Certificates, Supply bills etc. in the name of the bank is examples of assignment. The bank on whose name security rights are transferred by the assignor is called as assignee. On full payment of dues to the assignee, the assignor can get the security re-assigned in his name.

Relationship of Bailor and Bailee: Bailment refers to delivery of goods by one person to another for some purpose under a condition that the goods to be returned to depositor when the purpose is accomplished or otherwise disposed of according to the directions of the person while delivering the goods (Sec 148 of contract act). The person delivering the goods is known as bailor and the person to whom goods are delivered is called bailee.

## Collecting Banker Long Answer Type Questions

Question 1.
Explain the duties and responsibilities of collecting banker.
Answer:
The duties and responsibilities of a collecting banker are discussed below:
a) Due care and diligence in the collection of cheque.
b) Serving notice of dishonor.
c) Agent for collection.
d) Remittance of proceeds to the customer.
e) Collection of bill of exchange.
a) Due Care and Diligence in the Collection of Cheques:
The collecting banker is bound to show due care and diligence in the collection of cheques presented to him. In case a cheque is entrusted with the banker for collection, he is expected to show it to the drawee banker within a reasonable time. According to Section 84 of the Negotiable Instruments Act, 1881, “Whereas a cheque is not presented for payment within a reasonable time of its issue, and the drawer or person in whose account it is drawn had the right, at the time when presentment ought to have been made, as between himself and the banker; to have the cheque paid and suffers actual damage, through the delay, he is discharged to the extent of such damage, that is to say, to the extent to which such drawer or person is a creditor of the banker to a large amount than he would have been if such cheque had been paid.” In case a collecting banker does not present the cheque for collection through proper channel within a reasonable time, the customer may suffer loss. In case the collecting banker and the paying banker are in the same bank or where the collecting branch is also the drawee branch, in such a case the collecting banker should present the cheque by the next day. In case the cheque is drawn on a bank in another place, it should be presented on the day after receipt.

b) Serving Notice of Dishonour:
When the cheque is dishonoured, the collecting banker is bound to give notice of the same to his customer within a reasonable time. It may bcnoted here, when a cheque is returned for confirmation of endorsement, notice must be seni io his customer. If he fails to give such a notice, the collecting banker will be liable to the customer for any loss that the customer may have suffered on account of such failure.
Whereas a cheque is returned by the drawee banker for confirmation of endorsement, it is not called dishonour. But in such a case, notice must be given to the customer. In the absence of such a notice, if the cheque is returned for, the second time and the customer suffers a loss, the collecting banker will be liable for the loss.

c) Agent for Collection:
In case a cheque is drawn on a place where the banker is not a member of the ‘clearing-house’, hé may employ another banker who is a member of the clearinghouse for the purpose of collecting the cheque. In such a case the banker becomes a substituted agent. According to Section 194 of the Indian Contract Act, 1872, “Whereas an agent, holding an express or implied authority to name another person to act in the business of the agency has accordingly named another person, such a person is a substituted agent. Such an agent shall be taken as the agent of a principal for such part of the work as is entrusted to him.”

d) Remittance of Proceeds to the Customer: .
In casé a collecting banker has realised the cheque, he should pay the proceeds to the customer as per his (customer’s) direction. Generally, the amount is credited to the account of the customer on the customer’s request in writing, the proceeds may be remitted to him by a demand draft. In such circumstances, if the customer gives instructions to his banker, the draft may be forwarded. By doing so, the relationship between principal and agent comes to an end and the new relationship between debtor and creditor will begin.

e) Collection of Bills of Exchange:
There is no legal obligation for a banker to collect the bills of exchange for its customer. But, generally, bank gives such facility to its customers. In collection of bills, a banker. should examine the title of the depositor as the statutory protection under Section 131 of the Negotiable Instruments Act, 1881. Thus, the collecting banker must examine very carefully the title of his customer towards the bill. In case a new customer comes, the banker should extend this facility to him with a trusted reference.

Question 2.
Explain briefly the statutory protection given to collecting banker.
Answer:
The protection provided by Section 131 is not absolute but qualified. A collecting banker can claim protection against conversion if the following conditions are fulfilled:

1. Good Faith and Without Negligence :
Statutory protection is available to a collecting banker when he receives payment in good faith and without hegligence. The phrase in “good faith” means honestly and without notice or interest of dishonesty or fraud and does necessarily require carefulness. Negligence means failure to exercise reasonable care. The banker should have exercised reasonable care and deligence.
2. Collection for a Customer :
Statutory protection is available to a collecting banker if he collects on behalf of his customer only. If he collects for a stranger or noncustomer, he does not get such protection. A bank cannot get protéction when he.collects a cheque as holder for value
3. Acts as an Agent :
A collecting banker must act as an agent of the customer in order to get protection. He must receive the payment as an agent of the customer and not as a holder under independent title. The banker as a holder for value is not competent to claim protection from liability in conversion. In case of forgery, the holder for value is liable to the true owner of the cheque.
4. Crossed Cheques :
Statutory protection is available only in case of crossed cheques. It is not available in case uncrossed or open cheques because there is no need to collect them through a banker. Cheques, therefore, must be crossed prior to their presentment to the collecting banker for clearance.

## Collecting Banker Short Answer Type Questions

Question 1.
What are the duties of a collecting banker?
Answer:
The duties of collecting banker to customer are

1. He should undertake the collection of cheques bills, drafts etc.. on behalf of his customer.
2. He should present the cheque to the paying banker for encashment within a reasonable time.
3. He should examine the validity of the title of the customer to the cheque before accepting a cheque for collection
4. After collecting the cheque from, his customer collecting banker should handover the proceeds to the customer as a practicable in accordance with the instruction of the customer
5. In case the cheque presented for payment is dishonoured by the drawee or the paying banker the collecting banker shouldgive a notice of dishonour of the cheque to the customer with in a reasonable time go as to enable him to take the necessary steps to receive the amount of dishonoured cheque from the parties liable there to.
6. He should undertake the collection of cheque drafts billşetconly for his customer
7. For the collection of cheques the collecting banker should follow the normal or usual channel of collection so that delay in the collection of cheques can be avoided payment is honoured or realized
8. Incase of uncrossed cheque the duty collecting banker is to get them crossed by the customer and then accept them for collection
9. The collecting banker should check the correct non of the contents of the cheques like data amount in words and figures signature etc

Question 2.
What is holder for value? Explain?
Answer:
In case of open cheques when a banker acts as through he is a customer himself and collects the value of cheque from the paying banker the collecting banker will collect the cheques for himself as he will have already paid the value to the customer this position is called holder for value
The following circumstances under which a collecting banker becomes a holder for value

1. When the collecting banker collects the cheque and value of the cheque is paid to customer before it is actually collected
2. When collecting banker becomes the owner of the cheque accepted for collection
3. In case of holder for value collecting has rights of his own
4. When collecting banker collects the cheques for himself and not for the customer
5. When collecting banker acts as a holder for value he owes no duty to the customer
6. When collecting banker acts as holder for value if the presented cheque for payment become dishonourhe is required to give notice of dishonour to all the endorsers of the cheques so as to make them liable to him
7. Collecting banker gets better title to the cheque than that of customer from whom he received the cheques
8. In case of holder for value collecting banker is not entitled to the statutory protection

Question 3.
What is payment in due course? Explain?”.
Answer:
According to section 10 of Indian negotiable instrument act 1881 payment in due course means payment in accordance with the apparent tenor of the instrument in good faith without negligency to any person in possession there of under circumstances which do not afford a reasonable ground for believing that he is not entitiled to receive payment of the amount mentioned there in
The essential requirements of a payment in due course are

1. The payment should be made in accordance with the apparent tenor of the instrument
2. The payment should be made in good faith without negligency
3. The payment should be made to a person who is in possession of the cheque
4. The person to whom the payment is made should be in possession of the cheque under circumstances which do not afford a reasonable ground for believing that he is not entitled to receive the payment of the amount of the cheque.
5. The payment should be made in legal tender money only.

Question 4.
What is negligence? Give examples.
Answer:
The word ‘negligence’ means lack of proper care and attention. In banking the term negligence refers to lack of proper care and attention by the banker at the time of performing his duties. Examples:
The following are the instances of negligence on the part of the collecting Banker-

1. Failure to obtain introduction at the time of opening a current account in the name of a new customer.
2. Failure to follow up or check up the reference given by a new customer.
3. Acceptance of the reference of a stranger without ascertaining his bonafideness.
4. Failure to obtain the name of the married woman’s husband’s employer, while opening an account in the name of the customer.
5. Failure to verify the regularity or corresctness of endorsement on an order cheque or draft collected by him.
6. Faiļure to verify the existence of authority in the case of a proper endorsement.
7. Failure to make proper enquiries about the title of the customer to the cheque deposited for collection, when he is only the endorsee and not the payee.
8. Collection for an employee’s Private account the amount of a cheque payable to his employer.
9. Placing to an agent’s private account the amount of a cheque payable to the principal without making proper enquires
10. Collection for a trustee’s private account the amount of cheque payable to the trust without making proper enquiries.
11. Failure to make proper enquiries about the title of the party the cheque when a person of small or ordinary means deposits a cheque for large amount.
12. Collecting for a trustee’s directors, a managers or a secretary private account the amount of a cheque payable to the company without making proper enquires.

Question 5.
Distinguish between holder and holder in due course.
Answer:

1. Entitlement:
Holder is a person who is entitled for the possession of a negotiable instrument in his own name. Hence he shall receive or recover the amount due thereon. Whereas a Holder-in-due-course is a person who has obtained the instrument for consideration and in good faith and before maturity.
2. Consideration:
Consideration is not necessary to become a holder. The instrument may also be given by way of a donation or gift and thus, the donee of an instrument can also become a holder of it. However, consideration is a must to become a holder-in-due-course and thereby the donee of a negotiable instrument can be a holder but not holder-in-due course.
3. Maturity:
A holder may acquire the instrument even after its maturity. But a holder-in-due course must acquire the instrument before its maturity failing which he will not enjoy the rights of a holder-in-due-course.
4. Title:
A holder does not acquire a better title than that of transferor. In simple words, if the title of any of the prior party is defective, his title will not be defect free. Whereas, a holder-in-due-course derives a good title freed from all defects. His title is better than that of the transferor.
5. Right to recover amount:
A holder has a right to recover the amount due on the instrument from the transferor (i.e., just preceding party) only from whom he has obtained the instrument. Holderin-due-course, on the other hand, can recover the amount due on the instrument from any of the prior parties till the instrument is duly discharged. Thus, all prior parties shall remain liable towards the holder-in-due-course, jointly as well as severally, till – the instrument is duly discharged.
6. Notice of defect in the Title: A holder-in-due-course is not only supposed to have acquired the instrument without any notice of the defect of the title of the person from whom he obtained it, but also there should be no cause on his part to believe that any defect sustains in the transferor’s title. But a holder is exempt from this condition. He may have notice of defect in the title but he shall not be liable for it unless he is a party to that defect, fraud, or forgery.
7. Privileges:
A holder-in-due-course enjoys certain privileges under the Negotiable instruments Act which are not available to a holder.

## Paying Banker Very Short Answer Type Questions

Question 1.
Who is a paying banker?
Answer:
The banker who is liable to pay the value of a cheque of a customer as per the contract, when the amount is due from him to the customer is called “Paying Banker” or “Drawee Bank.” The payment to be made by him has arisen due to the contractual obligation. He is also called drawee bank as the cheque is drawn on him.

Question 2.
State the statutory protection given to paying banker.
Answer:
Section 85(1), 85(2), 128 of negotiable instrument acts provide statutory protection to paying banker for making payments of ordercheque, bearer cheque or crossed cheque in that order.

Question 3.
State any two precautions taken þy paying banker while making payment of cheques.
Answer:

1. Form of cheque
2. Protection regarding branch
3. Protection regarding account

Question 4.
What is mutilated cheque?
Answer:
A cheque is said to be mutilated when it is torn into two or more pieces. Such a cheque should not be paid unless the banker is satisfied that mutilation was unintentional and it also requires confirmations of the drawer.

Question 5.
Define cheque.
Answer:
As per negotiable instrument act 1881, A “cheque” is a bill of exchange drawn on a specified banker and not expressed to be payable otherwise than on demand.

Question 6.
State the parties to the cheque.
Answer:

1. Drawer
2. Drawee
3. Payee

Question 7.
State any two characteristics of cheque.
Answer:

1. Instrument in writing
2. Unconditional order
3. On a specified banker only

Question 8.
What is bearer cheque?
Answer:
Bearer cheques are the cheques which withdrawn to the cheque’s owner. These types of cheques normally used for a cash transaction.

Question 9.
What is order cheque?
Answer:
Order cheques are the cheques which are withdrawn for the payee(the person whose name is written on the cheque).

Question 10.
What is crossed cheque?
Answer:
On the Crossed cheques, two lines are made on the top right of the cheque. Amount: mentioned on the cheque is only transferred to the bank account of the payee. No cash payment is made.

Question 11.
State the difference between crossed cheque and account payee cheque.
Answer:
Crossed cheques can be endorsed to other parties while the Account-payee cheques can’t be endorsed and funds are only transferred to the account whose name is mentioned on the cheque.

Question 12.
What is stale cheque?
Answer:
In India, if a cheque is not presented to the bank within 3 months from the date written on the cheque is known as a stale cheque.

Question 13.
What is postdated cheque?
Answer:
If any cheque issued by a holder to the payee for the upcoming withdrawn date, then that type of cheques are called post-dated cheque.
For example – On 10 January 2019, Ram issued a cheque to Sham. Date written on the cheque is 10 February 2019.

Question 14.
Give the meaning of crossing.
Answer:
A crossing is an instruction to the paying banker to pay the amount of cheque to a particular banker and not over the counter. The crossing of the cheque secures the payment to a banker.

Question 15.
Give the meaning of general crossing.
Answer:
In general crossing, the cheque bears across its face an addition of two parallel transverse lines and/or the addition of words ‘and Co.’or ‘not negotiable’ between them.

Question 16.
Give the meaning of special crossing.
Answer:
In special crossing, the cheque bears across its face an addition of the banker’s name, with or without the words ‘not negotiable’.In this case, the paying banker will pay the amount of cheque only to the banker whose name appears in the crossing or to his collecting agent.

Question 17.
What is not negotiable crossing?
Answer:
It is when the words ‘Not Negotiable’ are written between the two parallel transverse lines across the face of the cheque in the case of general crossing or in the case of special crossing along with the name of a banker.

Question 18.
State any two advantages of cheque.
Answer:

1. It is an easy and convenient way of making large payment without using any cash and difficultly of counting.
2. Cheque is the safest mode of payment in case of any dispute in payment, it is easy to check the record involved in payment for the rectification of any error.
3. It is not only safest, but the cheapest way of making heavy payments even in the far areas of the country.

Question 19.
What is endorsement?
Answer:
Endorsement means signing at the back of the instrument for the purpose of negotiation. The act of the signing a cheque, for the purpose of transferring to the someone else, is called the endorsement of Cheque.

Question 20.
Define endorsement.
Answer:
According to Section 15 of the Negotiable Instruments Act 1881, When the maker or holder of a negotiable instrument signs the same, otherwise than as such maker, for the purpose of negotiation on the back or face thereof or on a slip of paper annexed thereto, or so signs for the same purpose a stamped paper intended to be completed as a negotiable instrument, he is said to endorse the same, and is called the “endorser”.

Question 21.
State the parties to endorsement.
Answer:
Endorsement involves two parties :
Endorser : The person making the endorsement.
Endorsee : The person to whom the instrument is endorsed.

Question 22.
State any two essentials of endorsement.
Answer:
Endorsement must be on the instrument itself. If no space is left on the instrument, it must be on a separate slip of paper and entered to the instrument. Endorsement may be made by the Endorser either by merely signing his name on the instrument or by specifying his name on the instrument or by specifying in addition to his signature on the person to whom on to whose order the instrument is payable. No particular form of words is necessary for the endorsement.

Question 23.
What is blank endorsement?
Answer:
An endorsement is said to be blank or general when the endorser puts his signature only on the instrument and does not write the name of anyone to whom or to whose order the payment is to be made.

Question 24.
What is conditional endorsement?
Answer:
The conditional endorsement is negotiation which takes effect on the happening of a stated event, or not otherwise. Section 52 of the Negotiable Instrument Act 1881 provides The endorser of a negotiable instrument may, by express words in the endorsement, exclude his own-liability thereon, or make such liability or the right of the endorsee to receive the amount due thereon depend upon the happening of a specified event, although such event may never happen.

Question 25.
What is restrictive endorsement?:
Answer:
Restrictive endorsement seeks to put an end the principal characteristics of a Negotiable Instrument and seals its further negotiability

Question 26.
What is facultative endorsement?
Answer:
Faculatative Endorsement is an endorsement where the endorser waives some right to which he is entitled.

Question 27.
State any two reasons for dishonor of cheqaue
Answer:
Amount in Words and Figures Bank dishonour the Cheque if amount written in words and figures are different. So, avoid this mistake.
Payee Name – If payee name is absent then bank can dishonor the Cheque with the reason that “Payee Name Required”.

## Banker and Customer Relationship Short Answer Type Questions

Question 1.
What are the precautions to be taken by the banker while opening and operating an account in the name of joint hindu family?
Answer:
Banker should take following steps to open and operate an account in the name of joint hindu family firm

1. Banker should ask for the names of all co-partners both major and minor and the other relevant particulars about the joint hindu family before opening an account.
2. Banker should collect the other details about manager of the family.
3. Banker should obtain signatures of all the major co-partceners on the account opening form.
4. Banker should open an account either in the name of joint family or in the name of the kartha.
5. Banker should get clear instructions about the persons authorized to operate the account of the family
6. Banker should obtain the signatures by all the major and adult co-parceners authorizing the kartha to operate the joint family account.
7. Banker should obtain the signatures of the guardians of the minor co-parceriers on all the bank documents on behalf of the minor co- parceners.
8. While giving advances to joint hindu family banker should enquire about exact purpose of the advances.
9. Banker should take great care to give advance against ancestral property of joint hindu family.
10. Kartha of the family is personally liable for the debts of the joint family to an unlimited extent banker should collect the loan document executed by the kartha as well as the other major co-parceners.

Question 2.
What are precautions to be takes by the banker to opened operate club’s account.
Answer:
Banker should take following precautions while opening an account in the name of club-

1. Banker should verify the registration certificate of the association or club and satisfy himself that the club is registered formally and properly.
2. He should obtain the copy of resolution of the managing committee of the club authorizing to open an account with the bank.
3. Banker should obtain name and specimen signature of officer bearer who are authorizied to operate club account.
4. Banker should obtain the club constitution bye laws to know about borrowing powers of the company.
5. Banker should examine the purpose of borrowing loan while giving loans to club.
6. Banker should know the personal account details of the office bears to compare it with club’s account.
7. Banker should receive a copy of resolution passed by the managing committee at the time of passed by the managing committee at the time of changing office beares to operate club’s account.

Question 3.
What precautions should a banker take while opening and conducting an accounting an account in the name of a married woman?
Answer:
The following precautions to be taken by the banker while opening and conducting an account in the name of a married woman.

1. The banker should avoid extending overdraft or granting loan to married woman.
2. It a banker is granted loan, banker shoulď secure sufficient property of hers which can be freely liquidated.
3. When she acts as an agent of her husband, the banker must see that she does not operate beyond the limit.
4. When loan is granted to a married women, the bank should ascertain whether she possesses and liquid atiable property.
5. In case of joint account held with her husband the banker should ascertain as to who would operate the account to whom the amount should be paid out on the death of any one of them.
6. Before granting an overdraft or a loan to a married women, it is better for the banker to require her to sign a free will clause.

Question 4.
Explain different types of bank account.
Answer:
There are four types of deposit accounts provided by banker to its customer they are
a) Current account
b) Saving account
c) Fixed deposit account
d) Recuring deposit account

a) Current account:
Current accounts are main accounts of commercial banks. Current accounts benefits are taken by commercial and industrial undertaking , public bodies, business etc this account is called as active account running its operations continuosly current account holde can depoit and withdraw the amount from his account for any number of times banker keeps major portion of current account deposit in liquid form to meet with drawls of the depositors large number of transactions are to be recorded in each current account

b) Saving bank account:
Bank also collects the savings amount from the public and opens savings bank amount to encourage the saving bank of the public. This account is usually opened by middle and small income group people this account is opened by the people to save their · part of current income for future purpose. Banker utilizes the savings account of his customer for other investment purpose therefore banker is giving attractive interest on the savings deposited amount

c) Fixed deposit account:
It is also called as time deposit account people deposit their amount in the fixed deposit account for particular term period. It is preferred by large number of investors because fixed deposit amount is risk free investment. Fixed deposit amount for a particular term period gives better income amount as interest to deposit holders. therefore people prefer to invest in fixed deposit account banker always uses entire deposit amount for profitable purposes.

d) Recurring deposit account:
Recurring deposit accounts are opened by fixed and regular income holder. In this type of account a predetermined amount is deposited into account every month the rate of interest is normally equal to the rate of interest payable on a term deposit account of the same period.

Question 5.
Explain the precautions to be taken while opening an account in the name of Association of person?
Answer:
Association is a non-trading concern registers its name under the companies act or the societies registration act. This association is called as an article person and gets a legal entity separate from that of its members. It can enter into contract in its own name and can use and be used. Banker has to take following precautions to open and operate an account in the name of association of persons.

1. Banker should examine the registration certificate of the association and should collect the copy of the same for verification.
2. Banker should obtain the copy of the bye law of association and examine the provisions relating to the bank accounts.
3. Banker should obtain the resolution copy to know about the name and designation of the person appointed to operate the account.
4. Banker should obtain personal security of one or more persons to grant advances and overdraft facility to such association.
5. Incase of un registered association the banker should take greater care and he should obtain security before sanctioning loans and advances.

Question 6.
Give a brief note on right of banker to close customer account.
Answer:
A customer may close the account with the banker at any time he feels without assigning any reason. Similarly, a banker may close the account of his customer by sending a written intimation to the customer. The banker must give the customer a sufficient notice before closing the account. If he closes the account without giving proper notice, he will dishonor cheques drawn before the closure of the account. This will injure the credit of the customer for which he may claim damages. The length of the notice will depend on the circumstances of the case and nature of the business of the customer. When a customer does not comply with the request of the banker to close his account even after the expiry of a reasonable notice given to him, the banker can close the account by returning the entire balance due to him. He must ask his customer to return the unused cheques. In the following cases, a banker can close the account of a customer without giving notice:

• When a customer dies, the banker must close the account of his customer on receiving a notice of death.
• When a banker comes to the knowledge that a customer has become insane, he should close his account.
• When a banker comes to the knowledge that a customer has become insane, he should close his account.
• A banker should not honor cheques after receiving the garnishee order from the court attaching his customer’s account in execution of a decree.
• When a banker receives a notice of assignment of his customer’s account to a third-party, he should not honor cheques issued after the assignment.

Question 7.
Explain the obligations of bank.
Answer:

1. Obligation to give notice before closing the account : A proper notice should be given to the customer, if a bank wants to close down the customer’s account. (It cannot close down due to serious consequences).
2. Obligation to maintain proper records : It is the duty of the banker to maintain proper and accurate records of all the transactions that customers made with the bank.
3. Obligation to follow customer’s instructions: Due to the contractual relationship that exists between the bank and customer, it is a legal obligation that the banker has to follow the customer’s instructions.
4. Obligation to maintain secrecy : No secrets should be disclosed by the bank to any third party regarding details of customer’s account because such disclosures may affect the credit of the.customer. Details can be revealed when practices amongst the banks permit such disclosure or when law requires such disclosures to be made.
5. Obligation to honour cheques : As bank is said to be the debtor of his customer, it has a statutory obligation that it has to honour cheques up to the amount standing to the credit of customer’s account. Bank has to compensate the customer, if it refuses in a wrong manner to honour cheques to its customer.

Question 8.
Explain the position of a minor as an account holder.
Answer:
All contracts entered into by a minor are void. Thus, a minor is not bound to repay money borrowed by him. Further he is entitled to recover any security pledged by him for the purpose of taking a loan. A minor can always pleas infancy and is not stopped to do so even when he has procured a loan or entered into some other contracts by falsely representing himself as a major (when he in reality was a minor).
Minor’s Position as an Account Holder.

1. Credit Account : An account can be opened in the name of a minor, and banker runs no risk so long as the account is in credit balance.
2. Unsecured Overdraft : The legal position of a contracts entered by a minor is void and therefore, he is not bound to pay the overdraft.
3. Secured Overdraft : The position of the banker is in no way better in the case of secured overdraft. Since he cannot avail any security given by a minor.
4. Overdraft Secured by Guarantee : Since a guarantee presupposes a debtor against whom the debt secured can be enforced to follow that a guarantee given to cover an overdraft given to a minor is void.
5. Joint Account : An account can be opened in the joint names of a minor and an adult. But, a minor cannot be made personally liable for an overdraft or loan
6. Minor as and Agent : He can act as an agent and as agent, if authorized to do so, he can draw, accept and enders bills which are binding on his principal, and may overdraw his principal’s account, if he is authorized in this regard. In all such cases the banker must obtain a clear mandate from the principal stating the various power given to the agent.
7. Minor as a partner : A minor may became a partner, but he is not personally liable for the debts of the partnership incurred during his minority.
8. Other Matters : Deposit account can be opened in the name or minors who can give a valid discharge for the money repaid to them. A minor may be appointed as executive, but he cannot act as such until he attains majority, and if sole executor, his duties meanwhile should be performed by his guardian of such other person as the court may appoint. But he cannot be appointed as a trustee.

A minor cannot make a valid will. If, therefore, a minor who has a banking account dies, any balance to his credit cannot be withdrawn until the letters of administration taken out by his next of kin are produced before the banker.

Question 9.
Distinguish between general lien and specific lien.
Answer:
Particular Lien

1. This right is available to bailee in respect of those goods only on which he has expended skill or labour.
2. This right can be exercised only to recover charges for skill or labour employed or expenses incurred on those goods
3. This right is available to bailee, finder of goods, inn-keepers, hoteliers, etc.

General Lien :

1. This right can be exercised against any property belonging to the other party in ::possession of the person exercising the right.
2. This right can be exercised for a general balance of account i.e., for any amount due.
3. This right is available only to bankers, factors wharfingers, attorneys of High Courts to and policy brokers.

## Banker and Customer Relationship Very Short Answer Type Questions

Question 1.
Define banking.
Answer:
As per Sec.5 (b) of the B R Act “Banking’ means accepting, for the purpose of lending or investment, of deposits of money from the public repayable on demand or otherwise and withdrawable by cheque, draft, order or otherwise.”

Question 2.
Who is a banker?
Answer:
“A banker or bank is a person or company carrying on the business of receiving money and collecting drafts for customers subject to the obligation of honoring cheques drawn upon them from time to time by the customer to the extent of the amount available on their àurrent accounts” Dr H.L.Hart.

Question 3.
State any two functions of banks.
Answer:

1. Accepting deposits
2. Collection of cheques and drafts
3. Conduct of stock exchange transaction
4. Preparation of income tax returns

Question 4.
Define customer.
Answer:
According to John Paget ‘To constitute a customer there must be some recognizable course or habit of dealing in the nature of regular banking business.”

Question 5.
State any two general relationship between banker and customer.
Answer:

1. Lessor and lessee
2. Bailor and bailee

Question 6.
State any two obligations of banker.
Answer:

1. Obligations to honour cheque
2. Obligations to maintain secrecy of customer

Question 7.
What is lien?
Answer:
Lien means the right of a creditor to retain in his possession the goods and securities owned by the debtor until the debit has been discharged, but not the right to sell.

Question 8.
What is general lien?
Answer:
General lien enables .a person to retain possession of goods belonging to another person for a general balance of account. Here the goods are not specific or particular.

Question 9.
What is particular lien?
Answer:
Particular lien is a specific lien which confers a right to retain those goods for which the amount is to be paid. Craftsman and mechanics enjoy specific lien. For example, a tailor has a particular lien for his stitching charges.

Question 10.
State any two exceptions to right of lien.
Answer:

1. Articles for safe custody
2. Documents left for a specific purpose.

Question 11.
What is right to set off?
Answer:
It is a statutory right available to a bank, to set off a debt owned to him by a creditor from the credit balances held in other accounts of the borrower. The right of set-off can be exercised only if there is no agreement express or implied to the contrary.

Question 12.
What is garnishee order.
Answer:
A court order instructing a garnishee (a bank) that funds held on behalf of a debtor (the judgement debtor) should not be released until directed by the court.

Question 13.
What is right of appropriation?
Answer:
It is the right of the customers to direct his banker against which debt (when more than one debt is outstanding the payment made by him should be appropriated. In case no such direction is given, the bank can exercise its right of appropriation and apply it in payment of any debt.

## Commercial Arithmetic Questions and Answers

Commercial Arithmetic Very Short Answer Type Questions

Question 1.
What is simple interest?
Answer:
It is the interest calculate for the principal amount for the time during which the money given is being used.

Question 2.
What is interest.
Answer:
Interest is the consideration which a borrower given to the lender for the money he has taken.

Question 3.
What is an amount.
Answer:
The total of principal and interest paid is called amount.

Question 4.
What is compound interest.
Answer:
Compound interest as the interest calculated on the principal and accrued interest.
Or
The interest produced after every fixed period is added to the principal for that amount we will again find the interest and the same procedure is continued till the stipulated time.
This type of interest is called compound interest.

Question 5.
Write the formula for simple interest and compound interest.
Answer:
Here both principal and compound interest change from time to time
SI = $$\frac{P R n}{100}$$ P = principal, R = rate, n = years
CI = A – P where A = P$$\left(1+\frac{R}{100}\right)^{n}$$

Question 6.
If simple interest on a certain sum is Rs. 360 for 2 years. @ 6% p.a. Find the sum.
Answer:
Given SI = 360 n = 2 years R = 6% P = ?
SI = $$\frac{P n R}{100}$$ ∴ P = $$\frac{S I \times 100}{n \times R}$$
= $$\frac{360 \times 100}{2 \times 6}$$
∴ P = 3,000

Question 7.
Find the compound interest on Rs. 2,560 for 3 years @ 8%.p.a.
Answer:
CI = A – P Given p = 2560, n = 3, R = 8%
A = P$$\left(1+\frac{R}{100}\right)^{n}$$
= 2560$$\left(1+\frac{8}{100}\right)^{3}$$
= 2560 (1.08)3
A = 3224.86
CI = A – P
= 3224.86 – 2560
CI = 664.86

Question 8.
Find the simple interest on Rs. 2276 for 2 years 6 months @ 12.5% p.a.
Answer:
SI = $$\frac{P n R}{100}$$ P = 2276, R = 12.5%, n = 2.5 years (2 years 6 months)
SI = $$\frac{2276 \times 2.5 \times 12.5}{100}$$ = 711.24

Question 9.
Find the SI on Rs. 285 for 21/2 years @3 percent. What is the amount after 21/2 years.
Answer:
P = 285, n = 2.5 years, R = 3%
SI = $$\frac{P R n}{100}=\frac{285 \times 2.5 \times 3}{100}$$ = 19.35
Amount A = P + SI = 285 + 19.35 = 304.35

Question 10.
Find the rate of interest for Rs. 200 to earn Rs. 80 interest for 5 years.
Answer:
Given p = 200, n = 5 years SI = 80, R = ?
SI = $$\frac{P n R}{100}$$ R = $$\frac{S 1 \times 100}{\mathrm{Pn}}$$
= $$\frac{80 \times 100}{200 \times 5}$$ = 8
R = 8%

Question 11.
What is Banker’s discount?
Answer:
The interest on the face value of the bill from the date of discounting to the due date of the bill is known as Banker’s Discount.

Question 12.
What is Bankers gain?
Answer:
The difference between the Bankers discount and the true discount is the banker’s gain.

Question 13.
Define Ratio?
Answer:
A ratio is the relationship between two quantities of the same kind. Ratio of a and bis written as a : b = $$\frac{a}{b}$$.

Question 14.
What do you mean by present value of Bill.
Answer:
The actual selling price is called the present value of bill.
Or
The value of a debt or a date prior to its due date is called the present value of Bill.
P = $$\frac{F}{1+r n}$$

Question 15.
What is proportion?
Answer:
If four quantities are such that the ratio of first & second is equal to the ratio of third & fourth, then the four quantities are said to be in proportion.

Question 16.
What is True Discount?
Answer:
Difference between the actual price and the sum due is called True Discount.
Or.
True discount is the simple interest on the present worth or original sum due.
TD = $$\frac{A n i}{1+n i}$$, n = no. of years, I = rate of interest

Question 17.
Find out 31/4% of Rs. 846.
Answer:
3 1/4% of Rs. 846 = $$\frac{13}{4}$$% of 846
= $$\frac{13}{4} \times \frac{1}{100}$$ × 846 = 27.495

Question 18.
How do you calculate fourth proportional to 6, 8, 9.
Answer:
Let x be the fourth proportional, then 6 : 8 = 9 : x
∴ 6x = 8 × 9 [product of extremes = product of means]
x = $$\frac{8 \times 9}{6}$$ = 12
x = 12

Question 19.
What is Direct proportion?
Answer:
Given two variable quantities, if one increases (decreases) the other quantity also increases (decreases), they are said to be Direct proportion.

Question 20.
What is inverse proportion.
Answer:
Given two variable quantities, if one increases (decreases) the other quantity decreases (increases), they are said to be inverse proportion.

Question 21.
What is Alternedo?
Answer:
The property a : b = c : d = a : c = b : d is called Alternedo property.

Question 22.
What is Bankers discount formula.
Answer:
B.D. = $$\frac{A n R}{100}$$ A = Amount, n = years, R = rate %

Question 23.
25% of a sum is 402.5. Find the sum.
Answer:
Let x be the sum
Then $$\frac{25}{100}$$ x x = 402.5
25x = 402.50 × 100
x = $$\frac{402.50 \times 100}{25}$$
x = 1610
∴ The sum = Rs. 1610

Question 24.
How much interest will be earned on Rs. 2,000/- @ 8.5% simple interest in 2 years.
Answer:
Simple interest SI = Pni = 2000 × 2 × $$\frac{8.5}{100}$$ = Rs. 340

Question 25.
Find out fourth proportional to the number 12, 16, 18.
Answer:
Fourth promportional to the numbers 12, 16, 18 is
Let the fourth proportional be x then 12 : 16 = 18 : x i.e. x = $$\frac{16 \times 18}{12}$$ = 24

Question 26.
Out of debt of Rs. 50,000, Rs. 18,000 has been paid what percent of the debt still remains unpaid?
Answer:
Balance of The debt to be unpaid = 50000 – 18000 = 32000
Percentage of the debt to be unpaid = $$\frac{32000}{50000}$$ × 100 = 64%

Commercial Arithmetic Short Answer Type Questions

Question 1.
2 Men & 4 boys can do a work in 33 days. How long shall 5 men & 2 boys take to finish it?
Answer:

 Men Boys Days 2 4 33 5 2 ?

Here unknown quantity is days and known quantities men and boys which are indirectly proportional to days.
∴ 2 + 4 ; 5 + 2 = x : 33
6 : 7 = x : 33
7x = 33 × 6
x = $$\frac{33 \times 6}{7}$$ = 28 days (approximately)

Question 2.
Mrs. Sheela borrowed Rs. 30,000 for 6 years. Calculate compound interest @ 12% p.a.reckoned quarterly.
Answer:
Given: P = 30,000
t = 6 years
r = 12/4 = 3%
∴ A = P$$\left(1+\frac{R}{100}\right)^{t}$$
= 30000$$\left(1+\frac{3}{100}\right)^{6 \times 4}$$ (because reckoned quarterly)
= 30,000 (1.03)24
= 60981
∴ C.I. = A – P=60981 – 30,000 = 30,981

Question 3.
In what period will Rs. 750 amount to Rs. 975 at 5% p.a. simple interest?
Answer:
Given = P = 750, A = 975, r = 5% t = ?.
S.I. = A – P = 975 – 750 = Rs. 225/-
PTR SI x 100
SI = $$\frac{P T R}{100}$$ ∴ T = $$\frac{S I \times 100}{\mathrm{PR}}$$
= $$\frac{225 \times 100}{750 \times 5}$$ = 6
∴ Time T = 6 years

Question 4.
A men lost 5% by selling an article for Rs. 28.50 for how much he should sell to gain 10%?
Answer:
Let the cost price be Rs. 100
The SP is Rs. 95 (i.e., 100 – 5)
Similarly if SP is Rs. 28.50 what is Cp?
CP SP
100 95
x = 28.5
∴ x = $$\frac{100 \times 28.50}{95}$$ = Rs. 30
The cost price is Rs. 30
To gain 10% = 30 + 10% of 30 = 30 + $$\frac{10}{100}$$ × 30 = 33
He should sell at Rs. 33.

Question 5.
After allowing a discount of 7 1/2% on the marked price of an article, an article is sold for Rs.555. Find its marked price.
Answer:
Let the marked price be 100
Less Discount 7.5%
Selling price = 92.50
If SP. Is 92.5 marked price = 100
If S.P. is 555 marked price = ?(x)
x = $$\frac{100 \times 555}{92.5}$$ = 600

Question 6.
At that rate present CI p.a. will be Rs. 640 amount to Rs. 774.40 in 2 years
Answer:
A = 774.40 p=640 n = 2 years r = ?

Question 7.
M. borrowed Rs. 12650 from a money lender a 18% p.a. simple interest. After 3 years, he paid 10381. He gave a buffalo to clear off the debt. What is the cost of buffalo?
Answer:
SI = $$\frac{P R n}{100}=\frac{12650 \times 3 \times 18}{100}$$ = 6831
Amount = SI + P = 6831 + 12650 = 19481
Amount = 19481
Cash paid = 10381 Difference = 9100
The cost of buffalo is Rs. 9100.

Question 8.
What is the face value of a bill discounted at 5% p.a. 73 days earlier than the date of maturity, the banker’s gain being Rs.10 only?
Answer:
B.G. = T.D. × n × $$\frac{r}{100}$$
10 = T.D. × $$\frac{73}{365} \times \frac{5}{100}$$
T.D. = Rs.1,000
BD = T.D. + B.G. = 1,000 + 10 = 1010
Face Value $$\frac{B D \times T D}{B G}=\frac{1000 \times 1010}{10}$$ RS.1,01,000.

Question 9.
If the bankers gain on certain bill due 6 months is Rs. 10 & the rate of interest 10% p.a. Find the face value of the bill.
Answer:

0.05A = 1.05(0.05A – 10)
0.05A = 0.0525A – 10.5
0.5A – 0.525A = 10.5
-0.0025A =-10.5 A = $$\frac{-10.5}{-0.025}$$
A = 4200 ∴ Face value of the bill = 4200/-

Question 10.
5 carpenters can earn Rs. 360 in 6 days working at 9 hours a day. How much will 8 carpenters can earn in 12 days working 6 hours a day?
Answer:

 Carpernters Days Hours Earn 5 6 9 360 8 12 6 ?

Ratio of carpenters 5 : 8 direct proportion
Ratio of days 6 : 12 direct proportion
Ratio of hours 9 : 6 direct proportion
∴ (5 × 6 × 9) : (8 × 12 × 6) = 360 : x
270 : 576 = 360 : x
270x = 360 × 576
x = $$\frac{360 \times 576}{270}$$ = 768

Question 11.
Find the difference between the S.I. and C.I. on Rs. 3,000 in 3 years at 4% p.a.
Answer:
Given P = 3000 n = 3 r = 4%
SI = $$\frac{p n r}{100}=\frac{3000 \times 3 \times 4}{100}$$
S.I. = Rs. 360
C.I. = A – P
A = P$$\left(1+\frac{r}{100}\right)^{n}$$
= 3000$$\left(1+\frac{4}{100}\right)^{3}$$
= 3000 (1.04)3
= 3000 × 1.124
A = 3374.592
C.1. = A – P
C.I. = 3374.592 – 3000
= 374.592
Difference between the S.I.& C.I. is 374.592-360 =14.592

Question 12.
A Banker discount bill which has to run 73 days before it is legally due at 6% p.a. & bankers gain is Rs. 60 for what sum the bill was drawn?
Answer:
R = 7% p.a. or for $$\frac{1}{5}$$ years. It is $$\frac{1}{5}$$ × 6 = $$\frac{6}{5}$$% = 1.2%
BG = SI or TD
TD = BG × $$\frac{100}{R}$$ = 60 × $$\frac{100}{1.2}$$ = 5000
∴ TD = 5000
BD = TD + BG
= 5000 + 60 = 5060
Bill Value = BD × $$\frac{100}{R}$$ = 5060 × $$\frac{100}{1.2}$$
Bill Value = Rs. 4, 21,666.

Question 13.
A man lost 8% by selling an article for Rs. 230. For how much should be has sold to gain 10%?
Answer:
Loss % = 8% SP = 230 Gain in % = 10%
Let the cost price (CP) of an article = x
Loss : Loss in% = $$\frac{\text { Loss }}{C P}$$ × 100
8 = $$\frac{\text { Loss }}{x}$$ × 100
Loss = $$\frac{8 x}{100}$$
Loss = CP – SP
$$\frac{8 x}{100}$$ = x – 230
8x = 100x – 230 × 100
100 × 230 = 92x
x = $$\frac{100 \times 230}{92}$$
x = 250
∴ the cost price = 250
Gain in % = $$\frac{\text { Gain }}{\text { C.P. }}$$ × 100 Gain = SP – CP
10 = $$\frac{S P-C P}{C P}$$ × 100
10 = $$\frac{S P-250}{250}$$ × 100
$$\frac{2500}{100}$$ = SP – 250
25 = SP – 250
25 + 250 = SP
∴ SP = 275
∴ He should have sold it for Rs. 275 to get 10% gain.

Question 14.
Raju borrowed Rs. 62,500 and paid Rs.67,600 in full settlement after 2 years. Find out the rate of compound interest.
Answer:
Given, P = Rs. 62,500, A = Rs. 67,600, T = 2years
C.I. = A – P = 67,600 – 62,500 = Rs. 5,100

$$\frac{R}{100}$$ = 1.04 – 1
R = 0.04 × 100 R = 4%

Question 15.
500 workers can finish a work in 8 days. How man workers will furnish the same work in 3 days.
Answer:
500 workers is 3 days
x workers is 3 days
more workers = less days=inverse proportion
500 x = 3 : 8
3x = 8 x 500
x = $$\frac{8 \times 500}{2} 1333.3$$
∴ Workers = 1333

Question 16.
A company’s yearly profits are found to have risen in the ratio 12 : 13 if in the previous year. The profits were Rs. 13,800. Find the profits this year?
Answer:
Let the profits in the previous year be 12x
And profits in the present year be 13x where x is the unit charge.
It is given that previous year profits = 13800
∴ 12x = 13800
x = $$\frac{13800}{12} \mathrm{x}$$ = 1150
Hence the present year profit= 13x
= 13 × 1150
= Rs. 14,950
The profit this year = Rs. 14,950.

Question 17.
A number is divided into 3 parts in the ratio 2 : 3 : 4 and if the 3rd part is 20 what are the others.
Answer:
Let the 3 parts be 2x, 3x & 4x respectively where x is the unit.
(Given) Third part is 20
4x = 20
x = $$\frac{20}{4}$$ = 5
∴ The 3. parts are 2x = 2 × 5 = 10
3x = 3 × 5 = 15
4x = 4 × 5 = 20

Question 18.
What would be the amount of Compound interest (CI) on Rs 5,000/- at 5% rate of interest p.a. for 3 years?
Answer:
Compound interest CI = A – P = P(1 + i)n — P = P[(1 + i)n – 1]
Where P = 5000, i = $$\frac{5}{100}$$ = 0.05, n = 3 yrs.
∴ CI = 5000 ((1.05)3 – 1] = 5000 [1.1576 – 1] = 5000[0.1576]
= Rs. 788.13

Question 19.
Find :
i) TD,
ii) BD,
iii) BG on a bill of Rs. 10,450 due 3 months hence @5% p.a.
Answer:

ii) BD = Ani = 10450 × 0.0125 = 130.625 ie Rs. 130.63
ii) BG = BD – TD = 130.63 – 129.01 = Rs. 1.62

Question 20.
Divide Rs. 1,600 between A, B and C, so that B may have Rs. 100 more than A and C Rs. 200 more than B.
Answer:
Let Share of A = A
Share of B = Rs. 100 more than A = A + 100
Share of C = Rs. 200 more than B = A + 100 + 200 = A + 300
But share of (A + B + C) = 1600
i.e. A + (A + 100) + (A + 300) = 1600
3A + 400 = 1600
3A = 1600 – 400
3A = 1200
A = $$\frac{1200}{3}$$ = 400
∴ Share of A = Rs. 400, Share of B = A + 100 = 400 + 100 = Rs. 500 and share of C = A + 300 = 400 + 300 = Rs. 700

Question 21.
Find the amount of annuity if payment of Rs. 300 is made at the end of each year, for 4 years at the rate of 10% p.a. compounded yearly.
Answer:
A = ?, P = 300, n = 4 yrs. i = $$\frac{10}{100}$$ =0.1.
Amount of annuity is
Amount of annuity = A = $$\frac{P}{i}$$[(1 + i)n – 1]
= $$\frac{300}{0.1}$$ (1.1)4 – 1] = 3000 [1.34431 – 1]
= 3000 [0.34431]
= Rs. 1032.93

Question 22.
A man had a certain sum of money. He gave 20% of it to his eldest son 30% of .: the remaining to his younger son and 10% of the remaining for poor boys in a school. Still he has Rs. 10,000 with him. Find his total sum.
Answer:
Let the money that man had be Rs. x
Share of eldest son= $$\frac{20}{100}$$ × x = 0.20x
Remaining = x – 0.20x = 0.80x
Share of younger son = 30% of the remaining
= $$\frac{30}{100}$$ × 0.80x = 0.24x
Then the remaining = 0.80x = 0.24x = 0.56x
Share of poor boys = 10% of the remaining = $$\frac{10}{100}$$ × 0.56x = 0.056x
Balance = 10,000
Now share of (eldest + younger + poor boys) + 10000 = x
0.20x + 0.24 × 0.56x + 10000 = x
0.496x + 10000 = x.
10000 = x – 0.496x
10000 = 0.504x i.e. $$\frac{1000}{0.504}$$ = x
i.e. 19841.27

Question 23.
A lady invested a total sum of Rs. 9,500 in two difference Banks which give 5% and 7 %2% simple interest. If both the amounts are going to be equal in 7 years. Find the individual investment.
Answer:
Total sum=9500 Here i1 = 5% = $$\frac{5}{100}$$ = 0.05, i2 = 7 1/2 % = $$\frac{7.5}{100}$$ = 0.075
Let the money invested in 5% simple interest= Rs. X
Then the money invested in 71/2% will be (9500 – x)
Then Amount A1 = principal + simple interest
A1 = P1 + P1ni1
= x + (x × 7 × 0.05) = x + 0.35x = 1.35x
A2 = P2 + P2nl2
A2 = (9500 – x) + (9500 – x) 7(0.075)
A2 = 9500 – x + (9500 – x) 0.525
A2 = 9500 – x + 4987.5 – 0.525x
A2 = 14487.5 – 1.525x
After 7 years A1 = A2
i.e. 1.35x = 14487.5 – 1.525x
1.35x + 1.525x = 14487.5
2.875x = 14487.5
x = $$\frac{14487.5}{1.825}$$ = 7938.36
∴ The sum invested at 5% = x = Rs. 7938.36
The sum invested at 7 72% = (9500 – x) = 9500 – 7938.36
= Rs. 1561.64

Question 24.
5 goldsmith can earn Rs. 48,000 in 6 days and working 8 hours per day. How much will 8 goldsmith earn in 12 days working 6 hour per day?
Answer:
Ratio of goldsmits = 5 : 6
Ratio of earning = 48000 : x
Ratio of days = 6 : 12
Ratio of hours = 8 : 6
Here 5 : 6 = 48000 : x (Direct proportion)
6 : 12 – 48000 : x (Direct proportion)
8 : 6 = 48000 : x (Direct proportion)
Then (5 × 6 × 8) ; (6 × 12 × 6) = 48000 : x
(5 × 6 × 8)x = (6 × 12 × 6) = 48000
x = $$\frac{6 \times 12 \times 6 \times 48000}{5 \times 6 \times 8}$$ = Rs. 86640

Commercial Arithmetic Long Answer Type Questions

Question 1.
Abill for Rs. 8,500 drawn on 25th April for 5 months was discounted on 17th July @ 5p.a. Find the discounted value of the bill.
Answer:
Due date is 25th April + 5 months + 3 days grace
28th September
No. of days from 17th July to 28th Sep. is
July = 14 days (excluding first day)
Aug = 31 days
Sep = 28 days
∴ N = 73 days
Discounted value of the bill = F.V – B.D.

Question 2.
The bankers gain on a bill due in 4 months discounted at 15% p.a is Rs. 360. Find
(i) True discount
(ii) Bankers discount
(iii) Face value of the bill.
Answer:
(i) True discount TD = $$\frac{B . G . \times 100}{\mathrm{NR}}$$
TD = $$\frac{360 \times 100}{\frac{4}{12} \times 15}$$ = 7200 TD = 7200
(ii) Banker Discount
BD = BD + TD
= 3600 + 7200 = 7560
(iii) Face value of the bill

Question 3.
A men left Rs. 1,30,000 for two sons aged 10 years and 16 years with the direction that the sum should be divided in such a way that the two sons get the same amount when they attain the age of 18 years. Assuming the rate of simple interest is 12 and half % p.a. Calculate how much the elder son got in the beginning.
Answer:
Let the share of the son aged 10 be x
Share of the son aged 16 = 1,30,000 – x
Date of maturity = each son is 18 years old.
Interval between maturity and present age 18 – 10 = 8 years
18 – 16 = 2 years
Amount of the son aged 10 = P + S.I. = x + $$\left(\frac{x \times 12.5 \times 8}{100}\right)$$
= x + x = 2x
Amount of the son aged 16 = P + S:I.
= (1,30,000 – x) + [1,30,000 – x) × $$\frac{12.5}{100}$$ × 2]
= (1,30.000 – x) + [(1,30,000 × x) × 0.25]
= 1,30,000 – x + 32500 – 0.25 x
= 162500 – 1.25x
∴ Rs. x are invested for 8 years and Rs. (1,30,000 – x) for 2 years and the respective amount are equal.
∴ 2x = 162500 – 1.25x
i.e., 162500 = 2x + 1.25x
3.25x = 162500
x = $$\frac{162500}{3.25}$$
x = 50,000
∴ the elder son share = 1,30,000 – x
1,30,000 – 50,000
= Rs. 80,000

Question 4.
Income of A and B are in the ratio of 7:5.and their expenditure is in the ratio of 9:8. An increase of A’s expenditure by Rs. 100 and decrease of B’s expenditure by Rs. 200 will make their savings of Rs. 400 each. Find their income & expenditure.
Answer:
Let the income be X and Expenditure be Y.
A & B’s income is in the ratio 7:5 and their expenditure is in the ratio 9:8.
Original savings ofA and B were :
A – 400 + 100 = Rs. 500
B – 400 – 200 = Rs. 200
Savings = Income – Expenditure.
i.e., 7x – 9y = 500 for A
and 5x – 8y = 200 for B
Solving Both eqn. [multiply Ist eqn by 5 & 2nd eqn by 7]
35x – 45y = 2500
35x – 56y = 1400
0 + 11y = 1100
∴ y = $$\frac{1100}{11} y$$ = 100
Substituting value in equationlst eqn.
7x – 9(100) = 500
7x – 900 = 500
7x = 500+ 900
7x = 1400.
x = $$\frac{1400}{7}$$ = 200x = 200
∴ Income of A is 7x = 7 × 200 = Rs. 1400
Income of B is 5x = 5 × 200 = Rs. 1000
Expenditure of A is 9y = 9 × 100 = Rs. 900
Expenditure of B is 8y = 8 × 100 = Rs. 800

Question 5.
A man sold 2 radios at Rs. 924 each. On one he gains 20% & on another the losses 20%. How much does he gain or loss on the whole transactions.
Answer:
I case SP = CP + profit
924 = x = 0.2x
924 = 1.2x
x = $$\frac{924}{1.2}$$ = 770
II case SP = CP – Loss
924 = x – 0.2x
924 = 0.8x
x = $$\frac{924}{0.8}$$ = 1155
∴ Profit 924 – 770 = 231
Loss = 1155 – 924 = 154
Net loss = 231 – 154 = 77

Question 6.
A sum of money lent out at SI amount to Rs. 3224 in 2 years & Rs. 4160 in 5 years. Find the sum of the rate of interest.
Answer:
Amount is 5 years = 4160
Amount in 2 years = 3224
Difference = 936 = interest for 3 years
∴ Interest for 1 year = $$\frac{936}{3}$$ = 312
For 2 years interest = 624
Principal = Amount – Interest
= 3324 – 624
= 2600
∴ R = $$\frac{100 \times S I}{p n}=\frac{100 \times 624}{2600 \times 2}$$ = 12%

Question 7.
On a bill of Rs. 20,750 due after 8 months at 6% p.a. Find
(i) Present value
(ii) 2. True discount,
(iii) Bankers discount,
(iv) Bankers gain.
Answer:

(iv) Bankers gain = BD – Td = 830 – 798.07 = 31.93

Question 8.
A sum of money amounts to Rs. 855 in 3 1/2 years at the rate of 4% p.a. simple interest. Find the sum.
Answer:
A = 855, n = 3.5 years; R = 4%, p = ?

85500 = 100P + 14P
85500 = 114P
P = $$\frac{85500}{114}$$ = 750
114 = 750
∴ Principal =Rs. 750

Question 9.
Mahesh spends 20% of his income for rent & 2/3 of the remainder for other expenses. If he saves Rs. 133.35 per month. Find the monthly income.
Answer:
Let the income of Mahesh be x.

Question 10.
The simple interest on a certain sum of money for 2 years is Rs.1,550 and the compound interest is Rs.1,588.75. Find the sum and the rate of interest.
Answer:
Let x be the principal
r = $$\frac{R}{100}$$ rate of interest
SI = 2x r = 1550 ……(1)
CI = x [(1 + r)2 – 1] = 1588.75 ….. (2)
Divde eqn 1 by eqn2

r2 + 2r = 2.05 r
r2 – 2.05r + 2r = 0
r2 – 0.05 r = 0
r(r – 0.05) = 0
r = 0 or r -0.05 = 0 r=0.05 ⇒ R = 5%
x = $$\frac{1550}{2 r}=\frac{1550}{2(0.05)}=\frac{1550}{0.1} x$$ = 15500
x – Principal – Rs. 15,500/- or R = 5%

Question 11.
A banker paid Rs.5,454 for a bill of Rs.5,500 drawn on 21st May due 6 months later. If the rate of interest is 6.1 p.a. Find the date on which the bill was discounted.
Answer:

 Day Month Date of Bill 21 5 Bill period 00 06 Naminal due date2 1 11 Grace period 03 00

∴ Legal due date 24 – 11
∴ Total days will be
Nov. 24 days
Oct. 30 days
50 days
∴ The bill was discounted on 5th October
Discounted value = Rs. 5,454
Face value = Rs. 5,500 – A
R = 6.1 % Bill period = 6 months
B.D. = face value – discounted value
= 5,500 – 5954 – 46 Rs.

∴ N = (0.1371 × 365) days
N = 50 days

Question 12.
Two numbers are in the ratio 5: 8. If 9 is added to each they are in the ratio 8 : 11. Find the numbers.
Answer:
Let the numbers be x and y.
x : y = 5 : b = $$\frac{x}{y}=\frac{5}{8}$$ ——– (1) ,
If 9 is added to each the numbers become 9 + x and 9 + y.
∴ The ratio of the new numbers is
$$\frac{9+x}{9+y}=\frac{8}{11}$$ ——– (2)
Solving (1) and (2) we get
8x = 5y
99 + 11x = 72 + 8y
Rearranging, we get
8x – 5y = 0 …….. (3)
11x – 8y = – 27 ……. (4)
Multiply 1st equation by 11 and equation 4 by 8.
88x – 55y = 0
88x – 64y = – 216

Question 13.
A man invested a total of Rs. 9500 in two different banks which give 5% and 712% simple interest. If both the amounts are going to be equal in 7 years find the individual investment.
Answer:
Let the two investments be x and y.
x + y = 9500 ——– (1)
No.: of years = 7, Rate at 1st Bank = 5%.
Rate at 2nd Bank = 71/2%.
Amount = P + Si

Solving (1) and (2) we get
y = 9500 – y …… (3)
Substitute eqn. 3 in eqn 2
135 (9500 – y) = 152.5y
1282500 – 135y = 152.5 y
1282500 = 152.5y + 135y
∴ y = $$\frac{1282500}{287.5}$$
y = 4460.869
x = 9500 – y
x = 9500 – 4460.9
x = 5039.1

Question 14.
A sum of money invested at C.I. amount to Rs. 2916 at the end of 2 years and to Rs. 3149.28 at the end of 3 years. Find the sum and rate of interest.
Answer:

Question 15.
a) If 12 pumps working 7 hours a day can lift 2,800 gallons of water in 20 days, in how many days can 20 pumps working 9 hours a day lift 3,000 gallons of water?
b) A bill for Rs. 14,600 drawn at 3 months was discounted on November 11th for Rs. 14,544. If the role of simple interest is 4% p.a., on what date was the bill drawn?
Answer:
a) Ratio of pumps = 12 : 20
Ratio of hours = 7 : 9
Ratio of gallons of water = 2800 : 3000
Ratio of days = 20 : x
Next 12 : 20 = x : 20 (inverse proportion) …… (1)
7 : 9 = x : 20 (inverse proportion) …… (2)
2800 : 3000 = 20 : x (direct proportion)
ie 3000 : 2800 = x : 20 ….. (3)
Compounding the ratios 12 × 7 × 3000 : 20 × 9 × 2800 = x : 20
⇒ $$\frac{12 \times 7 \times 3000}{20 \times 9 \times 2800}=\frac{x}{20}$$
ie x = $$\frac{12 \times 7 \times 3000 \times 20}{20 \times 9 \times 2800}$$ = 10 days

b) Face value of the bill = A= 14600
Date of discount=November 11th
BD = Banker’s Discount = 14600 – 14544 = 56
i = $$\frac{4}{100}$$ = 0.04
BD = Ani
1 + ni 56 = 14600 × n × 0.04
∴ $$\frac{56 \text { years }}{14600 \times 0.04}$$ = n ie n = $$\frac{56 \times 365}{14600 \times 0.04}$$ = 35 days
ie. No. of days from November 11th to due date = 35 days
No. of days from date of drawing to November 11th
= 90 – 35 = 55 days
Date of drawing = 55 days before Nov. 11th = 11 days (November) +31 days (October) + 13 days (September) = 16th September

Question 16.
a) A, B and Center into partnership with Rs. 50,000, Rs. 30,000 and Rs. 20,000 respectively. A and B get 20% and 10% of the profit for special efforts and the balance is share in capital ratio. In total if A receives Rs. 6,000 more than B. How much does each receive?
b) The difference between Banker’s discount and true discount on a bill due after 6
months at 4% p.a. interest being Rs. 20. Find
1) True discount
2) Banker’s discount
3) Present value
4) Face value of Bill
Answer:
a) Total = A + B + C = 50000 + 30000 + 20000 = 1000000
Let the profit of A, B and C = Rs.x
Special effort profit of A = $$\frac{20}{100}$$ of x = 0.2x
Special effort profit of B = $$\frac{10}{100}$$ of x = 0.1x
Balance remaining = x – (0.2x + 0.1x)
= x – 0.38 = 0.7x
∴ Total share of capital ratio = 0.7x
Investment ratio=50000 : 30000 : 20000
= 5 : 3 : 2
Total ratio = 5 + 3 + 2 = 10
Total profit of A = $$\left(\frac{5}{10} \times 0.7 x\right)$$ + 0.2x = 0.35x + 0.2x = 0.55x
Total profit of B = $$\left(\frac{3}{10} \times 0.7 x\right)$$ + 0.1x = 0.31x
Total profit of C = $$\frac{2}{10}$$ × 0.7x = 0.14x
But profit of A is 6000 more than B
∴ Total profit of B + 6000 = Total profit of A
0.31x + 6000 = 0.55x
6000 = 0.55 x – 0.31x
6000 = 0.24x
$$\frac{6000}{0.24}$$ = x ie x = 25000
i.e. Total profit of (A + B + C) = Rs. 25,000
Total profit of A = 0.55x = 0.55 × 25000 = Rs. 13750
Total profit of B = 0.31x = 0.31 × 25000 = Rs. 7750
Total Profit of C = 0.14x = 0.14 × 25000 = 5000 = Rs. 3500