Trade Discount

(46) If the banker’s discount on a bill is Rs. 300 and the rate of interest is 5%, 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: 9 months
• (c) Bill Amount: Rs. 6,500, Time Period: 8 months
• (d) Bill Amount: Rs. 5,500, Time Period: 12 months

Answer

Correct Answer: (a) Bill Amount: Rs. 6,000, 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 300 = \frac{P \cdot 5 \cdot T}{100}
Solving for P and T gives: P = Rs. 6,000 and T = 10 months.

(47) If the banker’s discount on a bill is Rs. 400 and the bill amount is Rs. 8,000, find the rate of interest and the time period.

• (a) Rate of Interest: 8%, Time Period: 6 months
• (b) Rate of Interest: 5%, Time Period: 12 months
• (c) Rate of Interest: 6%, Time Period: 9 months
• (d) Rate of Interest: 7%, Time Period: 8 months

Answer

Correct Answer: (b) Rate of Interest: 5%, Time Period: 12 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 400 = \frac{8000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 12 months.

(48) A bill for Rs. 7,500 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. 350, True Discount: Rs. 350
• (b) Banker’s Discount: Rs. 400, True Discount: Rs. 400
• (c) Banker’s Discount: Rs. 337.50, True Discount: Rs. 337.50
• (d) Banker’s Discount: Rs. 450, True Discount: Rs. 450

Answer

Correct Answer: (c) Banker’s Discount: Rs. 337.50, True Discount: Rs. 337.50
BD = \frac{P \cdot R \cdot T}{100} = \frac{7500 \cdot 9 \cdot \frac{4}{12}}{100} = Rs. 337.50
Since the time period is one-third of a year, the true discount is equal to the banker’s discount.
TD = BD = Rs. 337.50

(49) If the banker’s discount on a bill is Rs. 500, and the bill amount is Rs. 10,000, find the rate of interest and the time period.

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

Answer

Correct Answer: (d) Rate of Interest: 5%, Time Period: 6 months
Let the rate of interest be R% and the time period be T months.
BD = \frac{P \cdot R \cdot T}{100} \rightarrow 500 = \frac{10000 \cdot R \cdot T}{100}
Solving for R and T gives: R = 5% and T = 6 months.

(50) A bill for Rs. 3,600 is due in 6 months. The banker’s discount rate is 6% per annum. Find the banker’s discount and the true discount.

• (a) Banker’s Discount: Rs. 180, True Discount: Rs. 180
• (b) Banker’s Discount: Rs. 210, True Discount: Rs. 210
• (c) Banker’s Discount: Rs. 180, True Discount: Rs. 170.52
• (d) Banker’s Discount: Rs. 220, True Discount: Rs. 220

Answer

Correct Answer: (c) Banker’s Discount: Rs. 180, True Discount: Rs. 170.52
BD = \frac{P \cdot R \cdot T}{100} = \frac{3600 \cdot 6 \cdot \frac{6}{12}}{100} = Rs. 180
Since the time period is half a year, the true discount is not equal to the banker’s discount.
TD = \frac{BD \cdot 100}{R} = \frac{180 \cdot 100}{6} \approx Rs. 170.52