Question

The difference between the simple interest and the compound interest on a certain principal for $2$ years is $Rs.160$. If the simple interest is $Rs.2,880$, find the rate of interest.

Answer 1

Given : $|S.I.-C.I.|=160$ ..... $\left(i\right)$ $n=2$ ans $S.I.=Rs.2,880$

We know that,

$S.I.=\frac{P\times n\times R}{100}$

$⟹2880=\frac{P\times 2\times R}{100}$

$⟹\frac{PR}{100}=1440$ ........ $\left(ii\right)$

$|S.I.-C.I.|=P[{(1+\frac{R}{100})}^2-1]-2880$

$=P(\frac{R^2}{10000}+\frac{2R}{100})-2880$

$⟹160=\frac{PR}{100}(\frac{R}{100}+2)-2880$

$⟹3040=1440(\frac{R}{100}+2)$ ...... From $\left(i\right)$

$⟹\frac{R}{100}+2=\frac{3040}{1440}=\frac{19}{9}$

$⟹R=\frac{1}{9}\times 100=11.1\%$