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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. What is the time?
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- 3 months
- 4 months
- 5 months
- 6 months
Correct Option: B
On the basis of above given question , we can say that
Banker's Discount, BD = Simple Interest on the face value of the bill for unexpired time.
True Discount, TD = Simple Interest on the present value for unexpired time.
Simple Interest on Rs. 1600 = True Discount on Rs.1680
⇒ Rs. 1600 is the Present Worth (PW) of Rs. 1680
⇒ Rs. 80 is the Simple Interest of Rs.1600 at 15%
We know that ,
| Simple Interest = | PW x R x T | |
| 100 |
| 80 = | 1600 x 15 x T | |
| 100 |
⇒ 80 = 16 x 15 x T ⇒ 5 = 15 x T
| T = | 5 | year |
| 15 |
| T = | 12 | = 4 months |
| 3 |
