Trade Discount

(1) A bill for Rs. 1,200 is due in 6 months. The banker’s discount rate is 10% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 60, True Discount: Rs. 58
• (b) Banker’s Discount: Rs. 72, True Discount: Rs. 70
• (c) Banker’s Discount: Rs. 60, True Discount: Rs. 60
• (d) Banker’s Discount: Rs. 70, True Discount: Rs. 72

Answer

Correct Answer: (c) Banker’s Discount: Rs. 60, True Discount: Rs. 60
BD = \frac{P \cdot R \cdot T}{100} = \frac{1200 \cdot 10 \cdot \frac{1}{2}}{100} = Rs. 60
Since the time period is half a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 60

(2) If the banker’s discount on a certain sum due 9 months hence at 12% per annum is Rs. 108, what is the present value of the sum?

• (a) Rs. 2,700
• (b) Rs. 2,600
• (c) Rs. 2,800
• (d) Rs. 2,900

Answer

Correct Answer: (a) Rs. 2,700
BD = \frac{P \cdot R \cdot T}{100} \rightarrow P = \frac{BD \cdot 100}{R \cdot T} = \frac{108 \cdot 100}{12 \cdot \frac{3}{4}} = Rs. 2,700

(3) The true discount on a bill of Rs. 2,400 due 8 months hence is Rs. 160. What is the amount of money which the creditor must invest in order to be entitled to the bill after 4 months at 10% per annum?

• (a) Rs. 2,160
• (b) Rs. 2,260
• (c) Rs. 2,340
• (d) Rs. 2,240

Answer

Correct Answer: (d) Rs. 2,240
P = \frac{TD \cdot 100}{R \cdot T} = \frac{160 \cdot 100}{10 \cdot \frac{1}{3}} = Rs. 2,400
To find the investment amount:
Amount = P - TD = Rs. 2,400 - Rs. 160 = Rs. 2,240

(4) A bill of Rs. 6,000 is due in 4 months. If the banker’s discount rate is 12% per annum, find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 2,400, True Discount: Rs. 2,400
• (b) Banker’s Discount: Rs. 2,600, True Discount: Rs. 2,400
• (c) Banker’s Discount: Rs. 2,400, True Discount: Rs. 2,400
• (d) Banker’s Discount: Rs. 2,600, True Discount: Rs. 2,600

Answer

Correct Answer: (c) Banker’s Discount: Rs. 2,400, True Discount: Rs. 2,400
BD = \frac{P \cdot R \cdot T}{100} = \frac{6000 \cdot 12 \cdot \frac{4}{12}}{100} = Rs. 2,400
Since the time period is equal to the due date, the true discount is equal to the banker’s discount.
TD = BD = Rs. 2,400

(5) If the banker’s discount on a bill is Rs. 324 and the true discount is Rs. 300, find the bill amount and the rate of interest.

• (a) Bill Amount: Rs. 2,000, Rate of Interest: 12%
• (b) Bill Amount: Rs. 3,000, Rate of Interest: 10%
• (c) Bill Amount: Rs. 3,200, Rate of Interest: 8%
• (d) Bill Amount: Rs. 3,600, Rate of Interest: 6%

Answer

Correct Answer: (b) Bill Amount: Rs. 3,000, Rate of Interest: 10%
Let the bill amount be Rs. P and the rate of interest be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 324 = \frac{P \cdot R \cdot T}{100}
TD = BD - P = 324 - P = 300
Solving these equations gives: P = Rs. 3,000 and R = 10%