Question

The compound interest on a sum of money for two years is Rs 52 and the simple interest for two years at the same rate is Rs 50. Then the rate of interest is

• A. 6%
• B. 8%
• C. 9%
• D. 10%

Answer 1

The correct option is B 8%

Given,
Simple Interest for two years is 50
$\frac{P\times T\times R}{100}=SimpleInterest$
$\frac{P\times 2\times R}{100}=50$
$PR=2500$
$P=\frac{2500}{R}$................EQ(1)
Compound Interest for two years will be 52
$P{(1+\frac{r}{100})}^2-P=52$
$\Rightarrow P(1+\frac{2R}{100}+\frac{R^2}{10000}-1)=52$
$\Rightarrow P(\frac{2R}{100}+\frac{R^2}{10000})=52$
$\Rightarrow P\left(\frac{200R+R^2}{10000}\right)=52$
$\Rightarrow P\left(\frac{200R+R^2}{10000}\right)=52$
$\Rightarrow P(200R+R^2)=520000$
$\Rightarrow 200R+R^2=\frac{520000}{P}$
$\Rightarrow 200R+R^2=520000\times \frac{R}{2500}$(TAKING EQUATION FROM SIMPLE INTEREST EQ(1))
$\Rightarrow 200R+R^2=208R$
$\Rightarrow R^2=(208R-200R)$
$\Rightarrow R^2=8R$
$R=8$
Rate will be 8%