Question

# Simple interest on a certain sum is 1625 times of the sum invested. If the rate percent and time are numerically equal, then find the time .

A
8 years
B
6 years
C
4 years
D
9 years

Solution

## The correct option is A 8 yearsLet the sum invested be ₹ x. So, the interest earned  = ₹ 1625x. Let the time period be T years. So, the rate of interest = T% p.a. as the both time period and rate of interest are equal. The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R% p.a  is given by S.I=P× R× T100. By substituting given values, we get So, 16x25=x× T× T100⇒16x25=x× T2100⇒T2x100=16 x25⇒T2x=16x25×100⇒T2x=16x×4=64x⇒T2xx=64xx ⇒T2=64⇒T= ±8  Since time cannot be negative,we have time T=8 years.Hence, the correct option is A.

Suggest corrections