Trade Discount

(31) If the true discount on a bill of Rs. 7,200 due 9 months hence is Rs. 720, find the banker’s discount rate.

• (a) 10%
• (b) 8%
• (c) 12%
• (d) 15%

Answer

Correct Answer: (a) 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{9}{12}}{100} = Rs. 720
Solving for R gives: R = 10%

(32) If the banker’s discount on a bill is Rs. 480 and the rate of interest is 6%, find the bill amount and the time period.

• (a) Bill Amount: Rs. 8,000, Time Period: 12 months
• (b) Bill Amount: Rs. 7,500, Time Period: 8 months
• (c) Bill Amount: Rs. 9,000, Time Period: 10 months
• (d) Bill Amount: Rs. 6,000, Time Period: 9 months

Answer

Correct Answer: (a) Bill Amount: Rs. 8,000, 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 480 = \frac{P \cdot 6 \cdot T}{100}
Solving for P and T gives: P = Rs. 8,000 and T = 12 months.

(33) If the banker’s discount on a bill is Rs. 320, and the bill amount is Rs. 6,400, find the rate of interest and the time period.

• (a) Rate of Interest: 5%, Time Period: 10 months
• (b) Rate of Interest: 6%, Time Period: 8 months
• (c) Rate of Interest: 4%, Time Period: 12 months
• (d) Rate of Interest: 7%, Time Period: 6 months

Answer

Correct Answer: (a) 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 320 = \frac{6400 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 10 months.

(34) A bill for Rs. 8,000 is due in 4 months. The banker’s discount rate is 9% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 360, True Discount: Rs. 360
• (b) Banker’s Discount: Rs. 400, True Discount: Rs. 400
• (c) Banker’s Discount: Rs. 360, True Discount: Rs. 350
• (d) Banker’s Discount: Rs. 400, True Discount: Rs. 350

Answer

Correct Answer: (c) Banker’s Discount: Rs. 360, True Discount: Rs. 350
BD = \frac{P \cdot R \cdot T}{100} = \frac{8000 \cdot 9 \cdot \frac{4}{12}}{100} = Rs. 360
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{360 \cdot 100}{9} = Rs. 350

(35) If the banker’s discount on a bill is Rs. 560, and the bill amount is Rs. 12,000, find the rate of interest and the time period.

• (a) Rate of Interest: 7%, Time Period: 10 months
• (b) Rate of Interest: 6%, Time Period: 12 months
• (c) Rate of Interest: 8%, Time Period: 9 months
• (d) Rate of Interest: 9%, Time Period: 8 months

Answer

Correct Answer: (a) Rate of Interest: 7%, 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 560 = \frac{12000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 7% and T = 10 months.