Trade Discount

(36) A bill for Rs. 10,000 is due in 6 months. The banker’s discount rate is 6% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 350, True Discount: Rs. 350
• (b) Banker’s Discount: Rs. 400, True Discount: Rs. 400
• (c) Banker’s Discount: Rs. 300, True Discount: Rs. 300
• (d) Banker’s Discount: Rs. 450, True Discount: Rs. 450

Answer

Correct Answer: (c) Banker’s Discount: Rs. 300, True Discount: Rs. 300
BD = \frac{P \cdot R \cdot T}{100} = \frac{10000 \cdot 6 \cdot \frac{6}{12}}{100} = Rs. 300
Since the time period is half a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 300

(37) If the banker’s discount on a bill is Rs. 720, and the bill amount is Rs. 15,000, find the rate of interest and the time period.

• (a) Rate of Interest: 4%, Time Period: 9 months
• (b) Rate of Interest: 5%, Time Period: 8 months
• (c) Rate of Interest: 6%, Time Period: 10 months
• (d) Rate of Interest: 7%, Time Period: 7 months

Answer

Correct Answer: (a) Rate of Interest: 4%, 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 720 = \frac{15000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 4% and T = 9 months.

(38) A bill for Rs. 15,000 is due in 8 months. The banker’s discount rate is 6% 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. 900, True Discount: Rs. 900
• (c) Banker’s Discount: Rs. 720, True Discount: Rs. 700
• (d) Banker’s Discount: Rs. 900, True Discount: Rs. 700

Answer

Correct Answer: (c) Banker’s Discount: Rs. 720, True Discount: Rs. 700
BD = \frac{P \cdot R \cdot T}{100} = \frac{15000 \cdot 6 \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}{6} = Rs. 700

(39) If the banker’s discount on a bill is Rs. 960, and the bill amount is Rs. 16,000, find the rate of interest and the time period.

• (a) Rate of Interest: 6%, Time Period: 5 months
• (b) Rate of Interest: 5%, Time Period: 6 months
• (c) Rate of Interest: 7%, Time Period: 4 months
• (d) Rate of Interest: 8%, Time Period: 3 months

Answer

Correct Answer: (a) Rate of Interest: 6%, Time Period: 5 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 960 = \frac{16000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 6% and T = 5 months.

(40) A bill for Rs. 12,000 is due in 4 months. The banker’s discount rate is 5% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 250, True Discount: Rs. 250
• (b) Banker’s Discount: Rs. 300, True Discount: Rs. 300
• (c) Banker’s Discount: Rs. 250, True Discount: Rs. 240
• (d) Banker’s Discount: Rs. 300, True Discount: Rs. 240

Answer

Correct Answer: (c) Banker’s Discount: Rs. 250, True Discount: Rs. 240
BD = \frac{P \cdot R \cdot T}{100} = \frac{12000 \cdot 5 \cdot \frac{4}{12}}{100} = Rs. 250
Since the time period is one-third of a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{250 \cdot 100}{5} = Rs. 240