Question

The simple interest and the compound interest on a sum of money at a certain rate for $2$ year is $Rs.1,260$ and $Rs.1.323$ respectively.
Find the sum and the rate.

Answer 1

Simple Interest, S.I. = Rs. 1260 = $\frac{PR\times 2}{100}$ = $\frac{PR}{50}$ -(i)

Compound Interest, C.I. = Amount(A) - Principle(P)

=$P(1+\frac{R}{100}{)}^2$ - P = $PR(R/10000+1/50)=Rs.1323$ -(ii)

Dividing (ii) by (I),

$\frac{R}{200}+1$ = $\frac{1323}{1260}$

$\Rightarrow Rate,R=10$

Now, $\frac{PRT}{100}=1260$

$\Rightarrow$ $\frac{P\times 10\times 2}{100}=1260$

$\Rightarrow$ Principal or Sum , $P$ = Rs.$6,300$