Question

A sum of money becomes $\frac{8}{5}$ of itself in 5 years at a certain rate of simple interest. Find the rate of interest.

Answer 1

$$\begin{gathered} \begin{array}{l}\text{Let}\text{the sum be Rs.}x.\\ \text{Amount=}\frac{8x}{5}\\ \therefore \text{S}\text{.I}\text{.=A}-\text{P=}\frac{8x}{5}-x\\ \text{=}\frac{3x}{5}\\ \text{Let the rate be R}\%.\\ \text{S}\text{.I.=}\frac{\text{P×R×T}}{\text{100}}\\ =>\frac{3x}{5}=\frac{x\times \text{R}\times {\sout{5}}^1}{\sout{1}\sout{0}{\sout{0}}_{20}}\\ =>3x\times 20=\text{R}\times x\times 5\\ =>\text{R}=\frac{3\times \cancel{x}\times \sout{2}{\sout{0}}^4}{\cancel{x}\times \sout{5}}=12\end{array} \\ \mathrm{Hence},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{interest}\mathrm{is}12\%. \end{gathered}$$