Question

Mark (✓) against the correct answer
At simple interest a sum becomes $\frac{49}{40}$ of itself in $2\frac{1}{2}$ years. The rate of interest per annum is
(a) 7%
(b) 8%
(c) 9%
(d) 12%

Answer 1

(c) 9%
$\begin{array}{l}\text{Let the sum be Rs}x.\\ \\ \text{A}=\frac{49x}{40}\\ \text{We know:}\\ \text{A=P+S}\text{.I}\text{.}\\ \therefore \text{S}\text{.I. =A}-\text{P}\\ \text{=}(\frac{49x}{40}-x)\\ \text{=}\frac{49x-40x}{40}\\ \text{=}\frac{9x}{40}\\ \text{Let the rate be R}\%\text{per annum}.\\ \\ \text{S}\text{.I.=}\frac{\text{P}\times \text{R}\times \text{T}}{100}\\ =>\frac{9x}{40}=\frac{x\times \text{R}\times {\sout{5}}^1}{\sout{1}\sout{0}{\sout{0}}_{20}\times 2}\\ \text{=>R=}\frac{9\times \sout{2}{\sout{0}}^1\times {\sout{2}}^1}{\sout{4}{\sout{0}}_{{\sout{2}}_1}}\\ \text{=>R=9}\\ \end{array}$