Question

Mark (✓) against the correct answer
At simple interest a sum becomes $\frac{6}{5}$ of itself in $2\frac{1}{2}$ years. The rate of interest per annum is

(a) 6%
(b) $7\frac{1}{2}\%$
(c) 8%
(d) 9%

Answer 1

(c) 8%

$\begin{array}{l}\text{Let the sum be Rs.}x.\\ \text{Rate of interest =}r\%\\ \text{Time=2}\frac{\text{1}}{\text{2}}\text{years=}\frac{\text{5}}{\text{2}}\text{years}\\ \text{Amount=}\frac{\text{6}}{\text{5}}\text{× Sum}\\ \text{Rate=?}\\ \text{Amount =}\frac{\text{6}}{\text{5}}\text{×Sum}\\ \text{Principal + S}\text{.I}\text{. = Amount}\\ \text{Principal+}\frac{\text{Principal}\times \text{Rate×Time}}{\text{100}}\text{=}\frac{\text{6}}{\text{5}}\text{×Principal}\\ \text{=>}x\text{+}\frac{xr\times 5}{\text{100×2}}\text{=}\frac{\text{6}}{\text{5}}x\\ \text{=>}x\left(1\text{+}\frac{5r}{\text{100×2}}\right)=\frac{6}{5}x\\ \text{=>}1\text{+}\frac{r}{\text{40}}=\frac{6}{5}\\ =>r=40\times \frac{1}{5}\\ =>r=8\\ \text{So, the rate of interest is 8\%.}\end{array}$