Banker's Discount problems
- 1. The banker's discount on a certain sum due 2 years later is 11/10 of the true discount. the rate percent is?
Options- A. 11%
- B. 10%
- C. 5%
- D. 51/3 Discuss
Correct Answer: 5%
Explanation:
Let T.D. be Re. 1. Then, B.D. = Rs. (11/10) = Rs. 1.10
? Sum = Rs. 1.10 x 1/(1.10 - 1)
= Rs. 1.10 / 0.10 = Rs.11
So, S.I. on Rs. 11 for 2 years is Rs. 1.10
? Rate = (100 x 1.10) / (11 x 2)% = 5%
- 2. The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. Then the banker's discount is?
Options- A. Rs. 37
- B. Rs. 34.38
- C. Rs. 37.62
- D. Rs. 38.98 Discuss
Correct Answer: Rs. 37.62
Explanation:
B.G. = (T.D.)2 / P.W. = Rs. (36 x 36) / 800 = Rs. 1.62
? B.D. = (T.D.) + (B.G.) = Rs. (36 + 1.62)
= Rs. (37.62)
- 3. The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is?
Options- A. Rs. 60
- B. Rs. 150
- C. Rs. 108
- D. Rs. 110 Discuss
Correct Answer: Rs. 108
Explanation:
P.W. = Rs. (540 - 90) = Rs. 450
S.I. on Rs. 450 = Rs. 90
B.D. = S.I. on Rs. 540
= Rs. (90/450) x 540 = Rs. 108
- 4. The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 52 and Rs. 50, respectively. Find the sum and the rate percent?
Options- A. Rs. 1300, 6%
- B. Rs. 1200, 5%
- C. Rs. 1500, 8%
- D. None of these Discuss
Correct Answer: Rs. 1300, 6%
Explanation:
Sum = (B.D. x T.D.) / (B.D - T.D.) = (52 x 50) / 2 = Rs. 1300
Since B.D. is S.I. on sum due, so S.I. on Rs. 1300 for 8 months is Rs. 52 consequently.
Rate = [(100 x 52)] / [1300 x (2/3)] % = 6%
- 5. The banker's discount on Rs. 1600 at 6% is the same as the true discount on Rs. 1624 for the same time and at the same rate. Find the time?
Options- A. 3 months
- B. 4 months
- C. 6 months
- D. 8 months Discuss
Correct Answer: 3 months
Explanation:
S.I. on Rs. 1600 is P.W. of Rs. 1624
i.e. Rs. 24 is the S.I. on Rs. 1600 at 6%
? Time = (100 x 24) / (1600 x 6) = 1/4 year = 3 months
- 6. What rate percent does a man get for his money when in discounting a bill due 10 months hence he deducts 4% of the amount of the bill?
Options- A. 5%
- B. 6%
- C. 8%
- D. 4% Discuss
Correct Answer: 5%
Explanation:
Let the amount of bill be Rs. 100
Money deducted = Rs. 4
Money receive by holder of the bill = Rs. (100 - 4) = Rs. 96
S.I. on Rs. 96 for 10 months = Rs. 4
Rate = [(100 x 4 x 6) / (96 x 5)] = 5%
- 7. A banker's paid 5767.50 for a bill of Rs. 5840, drawn on April 4 at 6 months. On what day was the bill discounted the rate of interest being 7%?
Options- A. 3rd Aug.
- B. 4th Aug.
- C. 3rd Sep.
- D. 3rd July Discuss
Correct Answer: 3rd Aug.
Explanation:
B.D. = Rs. (5840 - 5767.20) = Rs. 72.80
Rs. 72.80 is S.I. on Rs. 5840 at 7%
So, Unexpired time = (100 x 72.80) / (7 x 5840) = 13/73 years = 65 days.
Now, date of draw o bill = April, 4 at 6 months.
Nominally due date = October 4.
Legally due date = October 7
So, we must go back 65 days from October 7.
Oct., sept., Aug. = 7 + 30 + 28
i.e., The bill was discounted on 3rd August.
- 8. The banker's discounted on a sum of money for 1 1/ 2 years is Rs. 60 and the true discount on the same sum for 2 years is Rs. 75. The rate percent is?
Options- A. 5%
- B. 6%
- C. 62 / 3%
- D. 31 / 3% Discuss
Correct Answer: 31 / 3%
Explanation:
B.D. for 3/2 years = Rs. 60
B.D. for 2 years = Rs. (60 x 2) / (3 x 2) = Rs. 80
Now, B.D. = Rs. 80, T.D. = Rs. 75 and Time = 2 years.
? Sum = Rs. (80 x 75) / 5 = Rs. 1200
? Rs. 80 is S.I. Rs. 1200 for 2 years.
So, rate = (100 x 80) / (1200 x 2)% = 31/3%
- 9. The face value of a bill due 5 yr hence is ? 13800. If the rate of simple interest is 5% per annum, what will be the banker's gain at the bill?
Options- A. ? 690
- B. ? 600
- C. ? 590
- D. ? 625 Discuss
Correct Answer: ? 690
Explanation:
Give that A = ? 13800 , R = 5%
T = 5 yr and BG = ?
According to the formula,
BG = [A(R x T)2] / [100(100 + R x T)]
= [13800(5 x 5)2] / [100(100 + 5 x 5)]
= (13800 x 625) / (100 x 125)
= ? 690
- 10. The true discount on a bill 24 months, hence at 24% per annum, is ? 144. What will be the banker's discount?
Options- A. ? 213.12
- B. ? 415
- C. ? 515.12
- D. ? 616 Discuss
Correct Answer: ? 616
Explanation:
Given that, R = 24%, T = 24 months= 2 yr and TD = ? 144
BD = TD + BG
According to the formula,
BG = (TD x R x T)/100 = (144 x 24 x 2)/100
= ? 69.12
? BD = 144 + 69.12 = ? 213.12
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