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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?
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- Sum = Rs. 400 and Time = 5 years
- Sum = Rs. 200 and Time = 2.5 years
- Sum = Rs. 400 and Time = 2.5 years
- Sum = Rs. 200 and Time = 5 years
Correct Option: C
As per the given question ,
BD = Rs.100 , TD = Rs.80 and R = 10%
| ∴ F = | ( BD × TD ) | |
| ( BD – TD ) |
| F = | ( 100 × 80 ) | |
| ( 100 – 80 ) |
F = ( 100 × 80 )/ 20
F = Rs. 400
Banker's Discount = Simple Interest on the face value of the bill for unexpired time
| Banker's Discount = | FTR | |
| 100 |
| ⇒ 100 = 400 × T × | 10 | |
| 100 |
⇒ 100 = 4 × T × 10
⇒ 10 = 4 × T
⇒ T = 10 /4
⇒ T = 2.5 years
