Trade Discount

(26) If the banker’s discount on a bill is Rs. 360 and the rate of interest is 6%, find the bill amount and the time period.

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

Answer

Correct Answer: (c) Bill Amount: Rs. 6,000, Time Period: 12 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 6 \cdot T}{100}
Solving for P and T gives: P = Rs. 6,000 and T = 12 months.

(27) If the banker’s discount on a bill is Rs. 240 and the bill amount is Rs. 4,800, find the rate of interest and the time period.

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

Answer

Correct Answer: (c) 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 240 = \frac{4800 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 10 months.

(28) A bill for Rs. 9,000 is due in 6 months. The banker’s discount rate is 8% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 600, True Discount: Rs. 600
• (b) Banker’s Discount: Rs. 720, True Discount: Rs. 720
• (c) Banker’s Discount: Rs. 360, True Discount: Rs. 360
• (d) Banker’s Discount: Rs. 450, True Discount: Rs. 450

Answer

Correct Answer: (c) Banker’s Discount: Rs. 360, True Discount: Rs. 360
BD = \frac{P \cdot R \cdot T}{100} = \frac{9000 \cdot 8 \cdot \frac{6}{12}}{100} = Rs. 360
Since the time period is half a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 360

(29) If the banker’s discount on a bill is Rs. 600, and the bill amount is Rs. 10,000, 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 600 = \frac{10000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 6% and T = 5 months.

(30) A bill for Rs. 4,500 is due in 3 months. The banker’s discount rate is 7% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 315, True Discount: Rs. 315
• (b) Banker’s Discount: Rs. 325, True Discount: Rs. 320
• (c) Banker’s Discount: Rs. 315, True Discount: Rs. 310
• (d) Banker’s Discount: Rs. 320, True Discount: Rs. 325

Answer

Correct Answer: (c) Banker’s Discount: Rs. 315, True Discount: Rs. 310
BD = \frac{P \cdot R \cdot T}{100} = \frac{4500 \cdot 7 \cdot \frac{3}{12}}{100} = Rs. 315
Since the time period is one-fourth of a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{315 \cdot 100}{7} = Rs. 310