Trade Discount

(6) A bill of Rs. 5,400 is due in 8 months. If the true discount is Rs. 600, find the banker’s discount rate.

• (a) 10%
• (b) 12%
• (c) 15%
• (d) 20%

Answer

Correct Answer: (b) 12%
Let the banker’s discount rate be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow BD = \frac{5400 \cdot R \cdot \frac{8}{12}}{100} = Rs. 600
Solving for R gives: R = 12%

(7) If the banker’s discount on a bill is Rs. 450, and the true discount is Rs. 400, find the time period.

• (a) 5 months
• (b) 6 months
• (c) 8 months
• (d) 10 months

Answer

Correct Answer: (d) 10 months
Let the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 450 = \frac{P \cdot R \cdot T}{100}
TD = BD - P = 450 - P = 400
Solving these equations gives: T = 10 months.

(8) If the banker’s discount is Rs. 360, and the rate of interest is 9%, find the bill amount and the time period.

• (a) Bill Amount: Rs. 4,000, Time Period: 12 months
• (b) Bill Amount: Rs. 3,600, Time Period: 10 months
• (c) Bill Amount: Rs. 4,000, Time Period: 10 months
• (d) Bill Amount: Rs. 4,500, Time Period: 9 months

Answer

Correct Answer: (c) Bill Amount: Rs. 4,000, 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 360 = \frac{P \cdot 9 \cdot T}{100}
Solving for P and T gives: P = Rs. 4,000 and T = 10 months.

(9) If the banker’s discount on a bill is Rs. 720, and the bill amount is Rs. 8,000, find the rate of interest and the time period.

• (a) Rate of Interest: 9%, Time Period: 10 months
• (b) Rate of Interest: 10%, Time Period: 12 months
• (c) Rate of Interest: 8%, Time Period: 8 months
• (d) Rate of Interest: 12%, Time Period: 6 months

Answer

Correct Answer: (a) Rate of Interest: 9%, 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 720 = \frac{8000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 9% and T = 10 months.

(10) A bill for Rs. 2,500 is due in 3 months. The banker’s discount rate is 15% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 400, True Discount: Rs. 400
• (b) Banker’s Discount: Rs. 425, True Discount: Rs. 420
• (c) Banker’s Discount: Rs. 375, True Discount: Rs. 375
• (d) Banker’s Discount: Rs. 410, True Discount: Rs. 410

Answer

Correct Answer: (c) Banker’s Discount: Rs. 375, True Discount: Rs. 375
BD = \frac{P \cdot R \cdot T}{100} = \frac{2500 \cdot 15 \cdot \frac{3}{12}}{100} = Rs. 375
Since the time period is one-fourth of a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 375