Question

The compound interest on a certain sum for $2$ years at $10\%$ per annum is Rs. $525$. The simple interest on the same for double the time at half the rate percent per annum is

• A. Rs. $4$00
• B. Rs. $600$
• C. Rs. $500$
• D. Rs. $800$

Answer 1

The correct option is C Rs. $500$

Let the sum be Rs. $x$.

Then $x[{(1+\frac{10}{100})}^2-1]=525$

$\Rightarrow x\left[{\left(\frac{11}{10}\right)}^2\right]=525$
$\Rightarrow x\left[\frac{121-100}{100}\right]=525$

$\Rightarrow x=\frac{525\times 100}{21}$ $=$ Rs. $2500$
For S.I., $P=$ Rs. $2500,R=5\%$ p.a. and $T=4$ years
Then S.I. $=$ Rs. $\left(\frac{2500\times 5\times 4}{100}\right)=$ Rs. $500$