Trade Discount

(56) If the banker’s discount on a bill is Rs. 450 and the bill amount is Rs. 9,000, 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: 9 months

Answer

Correct Answer: (d) Rate of Interest: 5%, 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 450 = \frac{9000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 9 months.

(57) A bill for Rs. 7,200 is due in 4 months. The banker’s discount rate is 8% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 256, True Discount: Rs. 256
• (b) Banker’s Discount: Rs. 288, True Discount: Rs. 288
• (c) Banker’s Discount: Rs. 192, True Discount: Rs. 192
• (d) Banker’s Discount: Rs. 320, True Discount: Rs. 320

Answer

Correct Answer: (c) Banker’s Discount: Rs. 192, True Discount: Rs. 192
BD = \frac{P \cdot R \cdot T}{100} = \frac{7200 \cdot 8 \cdot \frac{4}{12}}{100} = Rs. 192
Since the time period is one-third of a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 192

(58) If the true discount on a bill of Rs. 5,600 due 7 months hence is Rs. 700, find the banker’s discount rate.

• (a) 6%
• (b) 10%
• (c) 12%
• (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{5600 \cdot R \cdot \frac{7}{12}}{100} = Rs. 700
Solving for R gives: R = 10%

(59) If the banker’s discount on a bill is Rs. 375 and the bill amount is Rs. 7,500, 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: 9 months

Answer

Correct Answer: (d) Rate of Interest: 5%, 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 375 = \frac{7500 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 9 months.

(60) A bill for Rs. 8,400 is due in 5 months. The banker’s discount rate is 7% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 294, True Discount: Rs. 294
• (b) Banker’s Discount: Rs. 336, True Discount: Rs. 336
• (c) Banker’s Discount: Rs. 294, True Discount: Rs. 291.36
• (d) Banker’s Discount: Rs. 350, True Discount: Rs. 350

Answer

Correct Answer: (c) Banker’s Discount: Rs. 294, True Discount: Rs. 291.36
BD = \frac{P \cdot R \cdot T}{100} = \frac{8400 \cdot 7 \cdot \frac{5}{12}}{100} = Rs. 294
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{294 \cdot 100}{7} \approx Rs. 291.36