Trade Discount

(51) If the true discount on a bill of Rs. 7,200 due 8 months hence is Rs. 480, find the banker’s discount rate.

• (a) 4%
• (b) 10%
• (c) 12.5%
• (d) 15%

Answer

Correct Answer: (b) 10%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{7200 \cdot R \cdot \frac{8}{12}}{100} = Rs. 480
Solving for R gives: R = 10%

(52) If the banker’s discount on a bill is Rs. 350 and the rate of interest is 7%, find the bill amount and the time period.

• (a) Bill Amount: Rs. 5,000, Time Period: 8 months
• (b) Bill Amount: Rs. 5,000, Time Period: 10 months
• (c) Bill Amount: Rs. 6,000, Time Period: 12 months
• (d) Bill Amount: Rs. 6,500, Time Period: 6 months

Answer

Correct Answer: (b) Bill Amount: Rs. 5,000, Time Period: 10 months
Let the bill amount be Rs. P and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 350 = \frac{P \cdot 7 \cdot T}{100}
Solving for P and T gives: P = Rs. 5,000 and T = 10 months.

(53) If the banker’s discount on a bill is Rs. 600 and the bill amount is Rs. 12,000, find the rate of interest and the time period.

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

Answer

Correct Answer: (b) Rate of Interest: 5%, 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 600 = \frac{12000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 5 months.

(54) A bill for Rs. 5,000 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. 250, True Discount: Rs. 250
• (b) Banker’s Discount: Rs. 275, True Discount: Rs. 275
• (c) Banker’s Discount: Rs. 250, True Discount: Rs. 245.08
• (d) Banker’s Discount: Rs. 280, True Discount: Rs. 280

Answer

Correct Answer: (c) Banker’s Discount: Rs. 250, True Discount: Rs. 245.08
BD = \frac{P \cdot R \cdot T}{100} = \frac{5000 \cdot 6 \cdot \frac{6}{12}}{100} = Rs. 250
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{250 \cdot 100}{6} \approx Rs. 245.08

(55) If the true discount on a bill of Rs. 6,400 due 10 months hence is Rs. 640, find the banker’s discount rate.

• (a) 4%
• (b) 10%
• (c) 12.5%
• (d) 15%

Answer

Correct Answer: (b) 10%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{6400 \cdot R \cdot \frac{10}{12}}{100} = Rs. 640
Solving for R gives: R = 10%