Question

The difference between compound interest and simple interest on a sum for $2$ years at $8\%$ p.a is Rs. $768$. The sum is :

• A. Rs. $100000$
• B. Rs. $110000$
• C. Rs. $120000$
• D. Rs. $130000$

Answer 1

The correct option is C Rs. $120000$

$\Rightarrow$ Let the sum be $Rs.x$.

$\Rightarrow$ Then, $S.I=\frac{x\times 8\times 2}{100}=Rs.\frac{4x}{25}$ --- ( 1 )

$\Rightarrow$ $C.I=x\times (1+\frac{8}{100}{)}^2-x$

$\Rightarrow$ $C.I.=x\times (\frac{27}{25}{)}^2-x$

$\Rightarrow$ $C.I=\frac{729x}{625}-x=\frac{104x}{625}$ -- ( 2 )

$\Rightarrow$ $C.I-S.I=\frac{104x}{625}-\frac{4x}{25}=\frac{4x}{625}$ [From (1) and (2)]

$\therefore$ $768=\frac{4x}{625}$

$\therefore$ $x=\frac{768\times 625}{4}=Rs.120000$