Question

If the compound interest for 2 years on a certain sum be Rs 63 and the simple interest for 3 years on the same sum at same rate be Rs 90, then the sum will be

• A. Rs 300
• B. Rs 315
• C. Rs 325
• D. Rs 350

Answer 1

The correct option is A Rs 300

Given,
Simple Interest for three years is 90
$\frac{P\times T\times R}{100}=SimpleInterest$
$\frac{P\times 3\times R}{100}=90$
$3PR=9000$
$P=\frac{3000}{R}$................EQ(1)
Compound Interest for two years will be 63
$P{(1+\frac{r}{100})}^2-P=63$
$\Rightarrow P(1+\frac{2R}{100}+\frac{R^2}{10000}-1)=63$
$\Rightarrow P(\frac{2R}{100}+\frac{R^2}{10000})=63$
$\Rightarrow P\left(\frac{200R+R^2}{10000}\right)=63$
$\Rightarrow P\left(\frac{200R+R^2}{10000}\right)=63$
$\Rightarrow P(200R+R^2)=630000$
$\Rightarrow 200R+R^2=\frac{630000}{P}$
$\Rightarrow 200R+R^2=630000\times \frac{R}{3000}$(TAKING EQUATION FROM SIMPLE INTEREST EQ(1))
$\Rightarrow 200R+R^2=210R$
$\Rightarrow R^2=(210R-200R)$
$\Rightarrow R^2=10R$
$R=10$
Rate will be 10%
As per above equation EQ(1) principal amount will be $\frac{3000}{10}=300$
so sum will be Rs 300