Trade Discount

(41) If the banker’s discount on a bill is Rs. 720 and the bill amount is Rs. 12,000, find the rate of interest and the time period.

• (a) Rate of Interest: 4%, Time Period: 7 months
• (b) Rate of Interest: 5%, Time Period: 8 months
• (c) Rate of Interest: 6%, Time Period: 6 months
• (d) Rate of Interest: 7%, Time Period: 5 months

Answer

Correct Answer: (c) Rate of Interest: 6%, Time Period: 6 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 720 = \frac{12000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 6% and T = 6 months.

(42) A bill for Rs. 9,600 is due in 5 months. The banker’s discount rate is 8% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 320, True Discount: Rs. 320
• (b) Banker’s Discount: Rs. 400, True Discount: Rs. 400
• (c) Banker’s Discount: Rs. 320, True Discount: Rs. 310
• (d) Banker’s Discount: Rs. 400, True Discount: Rs. 310

Answer

Correct Answer: (c) Banker’s Discount: Rs. 320, True Discount: Rs. 310
BD = \frac{P \cdot R \cdot T}{100} = \frac{9600 \cdot 8 \cdot \frac{5}{12}}{100} = Rs. 320
Since the time period is five-twelfths of a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{320 \cdot 100}{8} = Rs. 310

(43) If the banker’s discount on a bill is Rs. 576 and the bill amount is Rs. 9,600, find the rate of interest and the time period.

• (a) Rate of Interest: 5%, Time Period: 9 months
• (b) Rate of Interest: 7%, Time Period: 8 months
• (c) Rate of Interest: 6%, Time Period: 9 months
• (d) Rate of Interest: 8%, Time Period: 7 months

Answer

Correct Answer: (c) Rate of Interest: 6%, Time Period: 9 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 576 = \frac{9600 \cdot R \cdot T}{100}
Solving for R and T gives: R = 6% and T = 9 months.

(44) A bill for Rs. 18,000 is due in 6 months. The banker’s discount rate is 9% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 1,350, True Discount: Rs. 1,350
• (b) Banker’s Discount: Rs. 1,800, True Discount: Rs. 1,800
• (c) Banker’s Discount: Rs. 1,350, True Discount: Rs. 1,320
• (d) Banker’s Discount: Rs. 1,800, True Discount: Rs. 1,320

Answer

Correct Answer: (c) Banker’s Discount: Rs. 1,350, True Discount: Rs. 1,320
BD = \frac{P \cdot R \cdot T}{100} = \frac{18000 \cdot 9 \cdot \frac{6}{12}}{100} = Rs. 1,350
Since the time period is half a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{1350 \cdot 100}{9} = Rs. 1,320

(45) If the true discount on a bill of Rs. 9,600 due 12 months hence is Rs. 1,200, find the banker’s discount rate.

• (a) 5%
• (b) 10%
• (c) 12.5%
• (d) 15%

Answer

Correct Answer: (c) 12.5%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{9600 \cdot R \cdot \frac{12}{12}}{100} = Rs. 1,200
Solving for R gives: R = 12.5%