Question

The compound interest on a sum for two years is Rs. $832$ and the simple interest on the same sum at the same rate for the same period is Rs. $800$. What is the rate of interest ?

• A. $6\%$
• B. $8\%$
• C. $10\%$
• D. $12\%$

Answer 1

Answer: (B)

$8\%$

Let the sum be Rs. $P$ and rate of interest per annum be $R\%$
Then $P[{(1+\frac{R}{100})}^2-1]-\frac{2PR}{100}=$ Rs. $832-$ Rs. $800=$ Rs. $32$
$\Rightarrow P[1+\frac{2R}{100}+\frac{R^2}{10000}-1]-\frac{2PR}{100}=32$
$\Rightarrow \frac{P{R}^2}{10000}=32$

$\Rightarrow PR\times R=320000$ ..........(i)
Also $\frac{2PR}{100}=800$ (S.I)

$\Rightarrow PR=40000$ .........(ii)
$\therefore$ From (i) and (ii), we have

$40000\times R=320000$

$\Rightarrow$ $R=8\%$ p.a.