A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both as interest. The rate of interest per annum is = ?

$$\eqalign{ & {\text{Let the rate }}\% {\text{ = R}} \cr & {\text{According to the question,}} \cr & \frac{{5000 \times 2 \times {\text{R}}}}{{100}} + \frac{{3000 \times 4 \times {\text{R}}}}{{100}} = 2200 \cr & \Rightarrow 100{\text{R}} + 120{\text{R}} = 2200 \cr & \Rightarrow 220{\text{R}} = 2200 \cr & \Rightarrow {\text{R}} = 10\% \cr & {\text{Hence required rate}}\% \cr & = 10\% \cr} $$