Question

If the ratio of Cl & SI interest for the same principal and rate of interest for $2$ years is $1:2$, find the rate of interest.

• A. $300$%
• B. $15$%
• C. $40$%
• D. $$3$%

Answer 1

The correct option is C $40$%

Given that,

principal $P$ and rate$R$ are same for 2 years.

$SI=\frac{PRT}{100}=\frac{P\times R\times 2}{100}$

$CI=A-P=P\left[\right(1+\frac{r}{100}{)}^T-1]=P[(1+\frac{R}{100}{)}^2-1]$

Given that,

$\frac{CI}{SI}=1.2$

$P\left[\right(1+\frac{R}{100}{)}^2-1]=1.2\times \frac{2\times PR}{100}$

$\frac{10000+R^2+200R}{10000}=\frac{24R+1000}{1000}$

$10000+R^2+200R=240R+10000$

$R^2=40R$

$R(R-40)=0$

$R=40$

Hence rate$\left(R\right)=40$

Option $\text{C}$ is correct.