Question

how much time will a sum of money double itsself if invested at 8% simple interest per annum

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{money}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Rate},\mathrm{R}=8\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},\mathrm{T}=? \\ \mathrm{Amount},\mathrm{A}=\mathrm{Rs}2\mathrm{x} \\ \mathrm{Now},\mathrm{SI}=\frac{\mathrm{PRT}}{100} \\ \Rightarrow \mathrm{A}-\mathrm{P}=\frac{\mathrm{PRT}}{100} \\ \Rightarrow 2\mathrm{x}-\mathrm{x}=\frac{\mathrm{x}\times 8\times \mathrm{T}}{100} \\ \Rightarrow \mathrm{T}=\frac{100}{8}=\frac{25}{2}=12\frac{1}{2} \\ \mathrm{So},\mathrm{required}\mathrm{time}=12\frac{1}{2}\mathrm{yrs} \end{gathered}$$