Question

Simple interest on a certain sum is $\frac{36}{25}$ of the sum. Find the rate per cent and time if they are both numerically equal.

• A. $12\%,10$ yrs
• B. $10\%,10$ yrs
• C. $12\%,12$ yrs
• D. $6\%,6$ yrs

Answer 1

Answer: (C)

$12\%,12$ yrs

Let the Principal be Rs. $x$

Then S.I. $=\frac{36x}{25}$
Let rate $=R\%$ per annum, then Time $=R$ years.
So S.I. $=\frac{P\times R\times T}{100}$

$⟹\frac{36x}{25}=\frac{x\times R\times T}{100}$
$⟹\frac{36\times 100}{25}=R^2$
$⟹R^2=36\times 4$
$⟹R=\surd \left(\begin{array}{c}36\times 4\end{array}\right)=6\times 2$
Therefore Rate $=12\%$ per annum and $T=12$ years