Question

Hira lent Rs 5000 to Sandeep for 2 years and 3000 to Shekharfor 4 years on simple interest at the same rate of interest and received Rs 22oo in all from both as interest. The rate of interest per annum is:

Answer 1

$$\begin{gathered} \mathbf{For}\mathbf{}\mathbf{Sandeep}\mathbf{}\mathbf{:} \\ \mathrm{Principal},{\mathrm{P}}_1=\mathrm{Rs}5000 \\ \mathrm{Time},{\mathrm{T}}_1=2\mathrm{yrs} \\ \mathrm{Rate},{\mathrm{R}}_1=? \\ \mathrm{Now},{\mathrm{I}}_1=\frac{{\mathrm{P}}_1{\mathrm{R}}_1{\mathrm{T}}_1}{100}=\frac{5000\times {\mathrm{R}}_1\times 2}{100}=\mathrm{Rs}100{\mathrm{R}}_1 \\ \mathbf{For}\mathbf{}\mathbf{Shekhar}\mathbf{:} \\ \mathrm{Principal},{\mathrm{P}}_2=\mathrm{Rs}3000 \\ \mathrm{Time},{\mathrm{T}}_2=4\mathrm{yrs} \\ \mathrm{Rate},{\mathrm{R}}_2=? \\ \mathrm{Now},{\mathrm{I}}_2=\frac{{\mathrm{P}}_2{\mathrm{R}}_2{\mathrm{T}}_2}{100}=\frac{3000\times {\mathrm{R}}_2\times 4}{100}=\mathrm{Rs}120{\mathrm{R}}_2 \\ \mathrm{Now},\mathrm{total}\mathrm{interest}=\mathrm{Rs}2200 \\ \Rightarrow {\mathrm{I}}_1+{\mathrm{I}}_2=2200 \\ \Rightarrow 100{\mathrm{R}}_1+120{\mathrm{R}}_2=2200 \\ \Rightarrow 100{\mathrm{R}}_1+120{\mathrm{R}}_1=2200\left[\mathrm{as}{\mathrm{R}}_1={\mathrm{R}}_2\right] \\ \Rightarrow 220{\mathrm{R}}_1=2200 \\ \Rightarrow {\mathrm{R}}_1=10 \\ \mathrm{So},\mathrm{rate}\mathrm{of}\mathrm{interest}=\mathbf{10}\mathbf{\%}\mathbf{}\mathbf{p}\mathbf{.}\mathbf{a}. \end{gathered}$$