Question

The simple interest in $3$ years and compound interest in $2$ years on a certain sum of money at the same rate are $Rs.1200$ and $Rs.832$ respectively. The principal is

• A. $Rs.7500$
• B. $Rs.4000$
• C. $Rs.3000$
• D. $Rs.5000$

Answer 1

The correct option is D $Rs.5000$

Compound interest for $2years=Rs.832$
Simple interest for $3years=Rs.1200$
As simple interest for each year remains the same.
So, simple interest for $2years=1200\times \frac{2}{3}=Rs.800$
We know that,
$C{I}_{2year}-S{I}_{2year}=\frac{S{I}_{2year}\times R}{200}=\frac{P{R}^2}{(100{)}^2}$
$832-800=\frac{800\times R}{200}$
$32=4\times R$
$R=8$%
Again, $C{I}_{2year}-S{I}_{2year}=\frac{P{R}^2}{(100{)}^2}$
$32=\frac{P\times (8{)}^2}{{100}^2}$
$32=\frac{P\times 64}{10000}$
$P=\frac{32}{64}\times 10000=5000$
Hence, the principal is $Rs.5000$.