Question

Simple interest on a certain sum is $\frac{16}{25}$ 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

Answer 1

The correct option is A 8 years

Let the sum invested be ₹ $x$.
So, the interest earned = ₹ $\frac{16}{25}$x.

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 $S.I=\frac{P\times R\times T}{100}$.
By substituting given values, we get
So, $\frac{16x}{25}=\frac{x\times T\times T}{100}$
$\Rightarrow \frac{16x}{25}=\frac{x\times T^2}{100}$
$\Rightarrow \frac{T^{2}x}{100}=\frac{16x}{25}$
$\Rightarrow T^{2}x=\frac{16x}{25}\times 100$
$\Rightarrow T^{2}x=16x\times 4=64x$
$\Rightarrow \frac{T^{2}x}{x}=\frac{64x}{x}$
$\Rightarrow T^2=64$
$\Rightarrow T=$ $\pm 8$
Since time cannot be negative,
we have time $T=8$ years.
Hence, the correct option is A.