Trade Discount

(16) If the banker’s discount on a bill is Rs. 500, and the true discount is Rs. 480, find the rate of interest.

• (a) 6%
• (b) 8%
• (c) 10%
• (d) 12%

Answer

Correct Answer: (b) 8%
Let the rate of interest be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 500 = \frac{P \cdot R \cdot T}{100}
TD = BD - P = 500 - P = 480
Solving these equations gives: R = 8%

(17) A bill of Rs. 4,000 is due in 4 months. If the banker’s discount is Rs. 320, find the true discount.

• (a) Rs. 240
• (b) Rs. 300
• (c) Rs. 280
• (d) Rs. 260

Answer

Correct Answer: (b) Rs. 300
Let the true discount be TD.
TD = BD - P = 320 - 4000 \cdot \frac{4}{12} \cdot \frac{8}{100} = Rs. 300

(18) If the banker’s discount on a bill is Rs. 480, and the rate of interest is 12%, find the bill amount.

• (a) Rs. 4,000
• (b) Rs. 4,200
• (c) Rs. 3,800
• (d) Rs. 4,500

Answer

Correct Answer: (a) Rs. 4,000
Let the bill amount be Rs. P.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 480 = \frac{P \cdot 12 \cdot \frac{1}{3}}{100}
Solving for P gives: P = Rs. 4,000

(19) A bill of Rs. 7,500 is due in 5 months. If the banker’s discount rate is 8% per annum, find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 300, True Discount: Rs. 300
• (b) Banker’s Discount: Rs. 350, True Discount: Rs. 340
• (c) Banker’s Discount: Rs. 300, True Discount: Rs. 300
• (d) Banker’s Discount: Rs. 340, True Discount: Rs. 350

Answer

Correct Answer: (c) Banker’s Discount: Rs. 300, True Discount: Rs. 300
BD = \frac{P \cdot R \cdot T}{100} = \frac{7500 \cdot 8 \cdot \frac{5}{12}}{100} = Rs. 300
Since the time period is five-twelfths of a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 300

(20) If the banker’s discount on a bill is Rs. 270, and the true discount is Rs. 250, find the bill amount and the rate of interest.

• (a) Bill Amount: Rs. 2,000, Rate of Interest: 12%
• (b) Bill Amount: Rs. 2,500, Rate of Interest: 10%
• (c) Bill Amount: Rs. 2,750, Rate of Interest: 8%
• (d) Bill Amount: Rs. 2,400, Rate of Interest: 15%

Answer

Correct Answer: (b) Bill Amount: Rs. 2,500, Rate of Interest: 10%
Let the bill amount be Rs. P and the rate of interest be R%.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 270 = \frac{P \cdot R \cdot T}{100}
TD = BD - P = 270 - P = 250
Solving these equations gives: P = Rs. 2,500 and R = 10%