Question

Simple interest on a certain amount is $\frac{16}{25}$ of the principal. If the number representing the rate of interest in percent and time in years be equal, then time, for which the principal amount is lent out, is:

• A. $5\frac{1}{2}$ years
• B. $6\frac{1}{2}$ years
• C. $6$ years
• D. $8$ years

Answer 1

The correct option is D $8$ years

Let the sum be $x$

Then, S.I. $=\frac{16x}{25}$

Let rate be $R\%$ and time be $R$ years

Therefore, $\frac{x\times R\times R}{100}=\frac{16x}{25}$

$\Rightarrow R^2=\frac{1600}{25}$

$\Rightarrow R=\frac{40}{5}=8$

Then rate of interest is $8\%$ and time for which the principal amount is lent out is $8$ years.