Question

The CI on a certain sum for $2$ years is Rs. $41$ and SI is Rs. $40$. Then, the rate percent per annum is:

• A. $4\%$
• B. $5\%$
• C. $6\%$
• D. $8\%$

Answer 1

Answer: (B)

$5\%$

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

Time $=2$ years

Then for C.I:

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

$\Rightarrow 41=P\left[\right(1+\frac{R}{100}{)}^2-1]$ .....$[\because (a+b{)}^2=a^2+b^2+2ab]$

$\Rightarrow 41=P[1+\frac{2R}{100}+\frac{R^2}{10000}-1]$

$\Rightarrow 41=\frac{2PR}{100}+\frac{P{R}^2}{10000}$

$\Rightarrow 41=\frac{PR}{50}+\frac{PR\ast R}{10000}$ ........(1)

For SI:

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

$\Rightarrow 40=\frac{PR2}{100}$

$\Rightarrow 40=\frac{PR}{50}$

$\Rightarrow PR=2000$

Put the value of $PR$ in (1),

$41=\frac{2000}{50}+\frac{2000}{10000}\times R$

$\Rightarrow 41=40+\frac{1}{5}R$

$\Rightarrow 41-40=\frac{1}{5}R$

$\Rightarrow R=1\times 5$

$\Rightarrow R=5\%$