The difference between S.I and C.I on a certain sum of money for 2 years at $12\frac{1}{2}\%$ p.a. is Rs.150. The sum is

Let the principle is $x\text{\hspace{0.17em}\hspace{0.17em}Rs.}$

Rate of interest $\text{R=12}\frac{1}{2}\%=\frac{25}{2}\%p.a$

Time $T=2\text{\hspace{0.17em}years}$

Simple interest $I_s=\frac{PTR}{100}$

$=\frac{x\times 2\times \frac{25}{2}}{100}$

$=\frac{x}{4}$

Amount on compound interest

$A=P{\left(1+\frac{{\displaystyle R}}{{\displaystyle 100}}\right)}^n$

But $A=x{\left(1+\frac{{\displaystyle \frac{{\displaystyle 25}}{{\displaystyle 2}}}}{{\displaystyle 100}}\right)}^2$

$A=x{\left(1+\frac{{\displaystyle 25}}{{\displaystyle 2\times 100}}\right)}^2$

$A=x{\left(1+\frac{{\displaystyle 1}}{{\displaystyle 8}}\right)}^2$

$A=x{\left(\frac{{\displaystyle 9}}{{\displaystyle 8}}\right)}^2$

$A=\frac{81x}{64}$

But $P+I=\frac{81x}{64}$

$I=\frac{81x}{64}-x$

$I_c=\frac{81x-64x}{64}$

$I_c=\frac{17x}{64}$

But $I_c-I_s=150$

$\frac{17x}{64}-\frac{x}{4}=150$

$\frac{17x-16x}{64}=150$

$x=64\times 150$

$x=Rs.9,600$