Banker's Discount problems
- 1.
The banker's discount on a certain sum due 2 years hence is 11 of the true discount. 10 The rate percent is:
Options- A. 11%
- B. 10%
- C. 5%
- D. 5.5% Discuss
Correct Answer: 5%
Explanation:
Let T.D. be Re. 1.
| Then, B.D. = Rs. | 11 | = Rs. 1.10. |
| 10 |
| ∴ Sum = Rs. | ❨ | 1.10 x 1 | ❩ | = Rs. | ❨ | 110 | ❩ | = Rs. 11. |
| 1.10 - 1 | 10 |
∴ S.I. on Rs. 11 for 2 years is Rs. 1.10
| ∴ Rate = | ❨ | 100 x 1.10 | ❩% | = 5%. |
| 11 x 2 |
- 2. The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Options- A. 3 months
- B. 4 months
- C. 6 months
- D. 8 months Discuss
Correct Answer: 4 months
Explanation:
S.I. on Rs. 1600 = T.D. on Rs. 1680.
∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
| ∴ Time = | ❨ | 100 x 80 | ❩year | = | 1 | year = 4 months. |
| 1600 x 15 | 3 |
- 3. The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Options- A. Rs. 400
- B. Rs. 360
- C. Rs. 480
- D. Rs. 320 Discuss
Correct Answer: Rs. 400
Explanation:
| T.D. |
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| = Rs. 400. |
- 4. The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:
Options- A. Rs. 36
- B. Rs. 72
- C. Rs. 48
- D. Rs. 96 Discuss
Correct Answer: Rs. 96
Explanation:
T.D. = √P.W. x B.G. = √576 x 16 = 96.
- 5. The banker's discount on a sum of money for 1½ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
Options- A. 10%
- B. 13%
- C. 12%
- D. 15% Discuss
Correct Answer: 12%
Explanation:
| B.D. for 3⁄2 years | = Rs. 558. | |||||||
| B.D. for 2 years |
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| = Rs. 744 |
T.D. for 2 years = Rs. 600.
| ∴ Sum = | B.D. x T.D. | = Rs. | ❨ | 744 x 600 | ❩ | = Rs. 3100. |
| B.D. - T.D | 144 |
Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.
| ∴ Rate = | ❨ | 100 x 744 | ❩% | = 12% |
| 3100 x 2 |
- 6.
The banker's gain on a certain sum due 1 1 years hence is 3 of the banker's 2 25 discount. The rate percent is:
Options- A.
5 1 % 5 - B.
9 1 % 11 - C.
8 1 % 8 - D.
6 1 % 6
Discuss
Correct Answer:
| 9 | 1 | % |
| 11 |
Explanation:
Let, B.D = Re. 1.
| Then, B.G. = Re. | 3 | . |
| 25 |
| ∴ T.D. = (B.D. - B.G.) = Re. | ❨ | 1 - | 3 | ❩ | = Re. | 22 | . |
| 25 | 25 |
| Sum = | ❨ | 1 x (22/25) | ❩ | = Rs. | 22 | . |
| 1-(22/25) | 3 |
| S.I. on Rs. | 22 | for 1 | 1 | years is Re. 1. |
| 3 | 2 |
| ∴ Rate = | ❨ | 100 x 1 | ❩% |
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- 7. 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. Rs. 20
- B. Rs. 24
- C. Rs. 16
- D. Rs. 12 Discuss
Correct Answer: Rs. 16
Explanation:
| B.G. = | (T.D.)2 | = Rs. | ❨ | 160 x 160 | ❩ | = Rs. 16. |
| P.W. | 1600 |
- 8. The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
Options- A. Rs. 480
- B. Rs. 520
- C. Rs. 600
- D. Rs. 960 Discuss
Correct Answer: Rs. 600
Explanation:
| T.D. = | ❨ | B.G. x 100 | ❩ | = Rs. | ❨ | 24 x 100 | ❩ | = Rs. 120. |
| Rate x Time | 10 x 2 |
| ∴ P.W. = | 100 x T.D. | = Rs. | ❨ | 100 x 120 | ❩ | = Rs. 600. |
| Rate x Time | 10 x 2 |
- 9. The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
Options- A. Rs. 72
- B. Rs. 36
- C. Rs. 54
- D. Rs. 50 Discuss
Correct Answer: Rs. 50
Explanation:
| T.D. = | B.G. x 100 | = Rs. | ❨ | 6 x 100 | ❩ | = Rs. 50. |
| R x T | 12 x 1 |
- 10. The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker's discount is:
Options- A. Rs. 37
- B. Rs. 37.62
- C. Rs. 34.38
- D. Rs. 38.98 Discuss
Correct Answer: Rs. 37.62
Explanation:
| B.G. = | (T.D.)2 | = Rs. | ❨ | 36 x 36 | ❩ | = Rs. 1.62 |
| P.W. | 800 |
∴ B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62
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