Trade Discount

(61) If the true discount on a bill of Rs. 8,800 due 6 months hence is Rs. 880, find the banker’s discount rate.

• (a) 6%
• (b) 8%
• (c) 10%
• (d) 12%

Answer

Correct Answer: (c) 10%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{8800 \cdot R \cdot \frac{6}{12}}{100} = Rs. 880
Solving for R gives: R = 10%

(62) A bill for Rs. 12,000 is due in 8 months. The banker’s discount rate is 9% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 720, True Discount: Rs. 720
• (b) Banker’s Discount: Rs. 720, True Discount: Rs. 648
• (c) Banker’s Discount: Rs. 800, True Discount: Rs. 800
• (d) Banker’s Discount: Rs. 900, True Discount: Rs. 900

Answer

Correct Answer: (b) Banker’s Discount: Rs. 720, True Discount: Rs. 648
BD = \frac{P \cdot R \cdot T}{100} = \frac{12000 \cdot 9 \cdot \frac{8}{12}}{100} = Rs. 720
Since the time period is two-thirds of a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{720 \cdot 100}{9} \approx Rs. 648

(63) If the banker’s discount on a bill is Rs. 500 and the bill amount is Rs. 10,000, find the rate of interest and the time period.

• (a) Rate of Interest: 4%, Time Period: 10 months
• (b) Rate of Interest: 5%, Time Period: 8 months
• (c) Rate of Interest: 6%, Time Period: 12 months
• (d) Rate of Interest: 5%, Time Period: 10 months

Answer

Correct Answer: (d) Rate of Interest: 5%, Time Period: 10 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 500 = \frac{10000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 10 months.

(64) A bill for Rs. 6,000 is due in 7 months. The banker’s discount rate is 8% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 280, True Discount: Rs. 280
• (b) Banker’s Discount: Rs. 336, True Discount: Rs. 336
• (c) Banker’s Discount: Rs. 280, True Discount: Rs. 270.55
• (d) Banker’s Discount: Rs. 350, True Discount: Rs. 350

Answer

Correct Answer: (c) Banker’s Discount: Rs. 280, True Discount: Rs. 270.55
BD = \frac{P \cdot R \cdot T}{100} = \frac{6000 \cdot 8 \cdot \frac{7}{12}}{100} = Rs. 280
Since the time period is seven-twelfths of a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{280 \cdot 100}{8} \approx Rs. 270.55

(65) If the true discount on a bill of Rs. 9,600 due 9 months hence is Rs. 960, find the banker’s discount rate.

• (a) 5%
• (b) 7%
• (c) 10%
• (d) 12%

Answer

Correct Answer: (c) 10%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{9600 \cdot R \cdot \frac{9}{12}}{100} = Rs. 960
Solving for R gives: R = 10%