Banker's Discount problems
- 1. The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?
Options- A. Sum = Rs.400 and Time = 5 years
- B. Sum = Rs.200 and Time = 2.5 years
- C. Sum = Rs.400 and Time = 2.5 years
- D. Sum = Rs.200 and Time = 5 years Discuss
Correct Answer: Sum = Rs.400 and Time = 2.5 years
Explanation:
BD = Rs.100
TD = Rs.80
R = 10%
BD = Simple interest on the face value of the bill for unexpired time= FTR/100
=> T = 2.5 years
- 2. A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.
Options- A. 4390
- B. 6580
- C. 5880
- D. 5350 Discuss
Correct Answer: 5880
Explanation:
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.
Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.
- 3. The bankers discount and true discount on a sum of money due 8 months hence are Rs.120 & Rs.110 resp. Find the sum.
Options- A. 1457
- B. 1320
- C. 1140
- D. 1260 Discuss
Correct Answer: 1320
Explanation:
Sum = (B.D * T.D) / (B.D) -(T.D)
= (120 * 110) / (120 -110)
= 1320
- 4. If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?
Options- A. 8 months
- B. 11 months
- C. 10 months
- D. 9 months Discuss
Correct Answer: 9 months
Explanation:
F = Rs. 498
TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5%
=> T = 3/4 years = 9 months
- 5. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain.
Options- A. Rs.145
- B. Rs.136
- C. Rs.121
- D. Rs.112 Discuss
Correct Answer: Rs.121
Explanation:
T.D. =Ö(P.W.*B.G)
B.G. =(T.D.)2/ P.W.
= Rs.[(110x110)/ 1100]
= Rs. 11.
B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
- 6. The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is:
Options- A. 15
- B. 16
- C. 14
- D. 13 Discuss
Correct Answer: 16
Explanation:
B.G. =(T.D.)^2/P.W.
= Rs. (160*160)/1600 = Rs. 16.
- 7. If the true discount on a certain sum due 6 months hence at 15% is Rs 120.What is the bankers discount on the same for same time and the same rate.
Options- A. Rs.109
- B. Rs.119
- C. Rs.129
- D. Rs.139 Discuss
Correct Answer: Rs.129
Explanation:
B.G = S.I On T.D
= Rs. (120 * 15 * 1/2 * 1/100)
= Rs.9
B.D - T.D = Rs.9
B.D = Rs.(120 +9) = Rs.129
- 8. The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?
Options- A. Rs. 432
- B. Rs. 422
- C. Rs. 412
- D. Rs. 442 Discuss
Correct Answer: Rs. 432
Explanation:
F = Rs. 2160
TD = Rs. 360
PW = F - TD = 2160 - 360 = Rs. 1800
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=(360/1800)* 2160
= (1/5) * 2160
=Rs. 432
- 9. The banker's discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?
Options- A. Rs. 24
- B. Rs. 12
- C. Rs. 36
- D. Rs. 18 Discuss
Correct Answer: Rs. 18
Explanation:
T= 6 months = 1/2 year
R = 6%
- 10. What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5%
Options- A. Rs. 2
- B. Rs. 1.25
- C. Rs. 2.25
- D. Rs. 0.5 Discuss
Correct Answer: Rs. 1.25
Explanation:
F = Rs. 8100
R = 5%
T = 3 months = 1/4 years
Therefore BD - TD = 101.25-100 = Rs.1.25
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