Question

The SI on a sum of money for $3$ years is Rs. $480$ and the CI on the sum at the same rate for $2$ years is Rs. $340$. The rate % p.a. is:

• A. $16\%$
• B. $12\frac{1}{2}\%$
• C. $13\frac{1}{2}\%$
• D. $12$

Answer 1

The correct option is B $12\frac{1}{2}\%$

$SI=\frac{P\times r\times t}{100}$

$⟹480=\frac{P\times r\times 3}{100}$

$P=16000/r$

$CI=P(1+\frac{r}{100}{)}^n-P$

$340=P\left[\right(1+\frac{r}{100}{)}^2-1]$

$340=\left(16000/r\right)\left[\right(1+\frac{r}{100}{)}^2-1]$

Solving for we get, $r=25/2\%$