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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 .


Correct Answer
A
8 years
Your Answer
B
6 years
Your Answer
C
4 years
Your Answer
D
9 years

Solution

The correct option is A 8 years
Let 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.

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