Question

The CI on a certain sum for $2$ years is Rs. $410$ and SI is Rs. $400$. The rate of interest per annum is:

• A. $10\%$
• B. $8\%$
• C. $5\%$
• D. $4\%$

Answer 1

The correct option is C $5\%$

Let the principle is Rs. $P$ and rate of interest is $R\%$

Time $=2$ years

Then for C.I

CI $=P{(1+\frac{R}{100})}^2-P$

$\Rightarrow 410=P[{(1+\frac{R}{100})}^2-1]$ ....$[\because {(a+b)}^2=a^2+b^2+2ab]$

$\Rightarrow 410=P[1+\frac{2R}{100}+\frac{R^2}{10000}-1]$

$\Rightarrow 410=\frac{2PR}{100}+\frac{P{R}^2}{10000}$

$\Rightarrow 410=\frac{PR}{50}+\frac{PR\ast R}{10000}$........1

For SI:

$SI=\frac{PRT}{100}$

$\Rightarrow 400=\frac{PR2}{100}$

$\Rightarrow 400=\frac{PR}{50}$

$\Rightarrow PR=20000$

Put the value of $PR$ in (1)

$410=\frac{20000}{50}+\frac{20000}{10000}\times R$

$\Rightarrow 410=400+2R$

$\Rightarrow 410-400=2R$

$\Rightarrow R=\frac{10}{2}$

$\Rightarrow R=5\%$