Question

A sum of money put at 9% per annum simple interest amount to Rs 10160 in 3 years . What will it amount to in 2 years at 8% per annum rate

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{P}\mathrm{be}\mathrm{the}\mathrm{principal}. \\ \mathrm{Rate},{\mathrm{R}}_1=9\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},{\mathrm{T}}_1=3\mathrm{yrs} \\ {\mathrm{I}}_1=\frac{{\mathrm{PR}}_1{\mathrm{T}}_1}{100} \\ \Rightarrow {\mathrm{A}}_1-\mathrm{P}=\frac{{\mathrm{PR}}_1{\mathrm{T}}_1}{100} \\ \Rightarrow 10160-\mathrm{P}=\frac{\mathrm{P}\times 9\times 3}{100} \\ \Rightarrow 10160-\mathrm{P}=\frac{27\mathrm{P}}{100} \\ \Rightarrow \frac{27\mathrm{P}}{100}+\mathrm{P}=10160 \\ \Rightarrow \frac{127\mathrm{P}}{100}=10160 \\ \Rightarrow \mathrm{P}=8000 \\ \mathrm{so},\mathrm{required}\mathrm{principal}=\mathrm{Rs}8000 \\ \mathrm{Now},{\mathrm{R}}_2=8\%\mathrm{p}.\mathrm{a}. \\ {\mathrm{T}}_2=2\mathrm{yrs} \\ \mathrm{Now},{\mathrm{I}}_2=\frac{{\mathrm{PR}}_2{\mathrm{T}}_2}{100}=\frac{8000\times 8\times 2}{100}=\mathrm{Rs}1280 \\ {\mathrm{A}}_2=\mathrm{P}+{\mathrm{I}}_2=8000+1280=\mathrm{Rs}9280 \end{gathered}$$