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 of them as interest. The rate of interest per annum is:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{rate}}\,{\text{be}}\,R\% \,{\text{p}}{\text{.a}}{\text{.}}\,{\text{Then,}} \cr & {\frac{{5000 \times R \times 2}}{{100}}} + {\frac{{3000 \times R \times 4}}{{100}}} \cr & = 2200. \cr & \Rightarrow 100R + 120R = 2200 \cr & \Rightarrow R = {\frac{{2200}}{{220}}} = 10 \cr & \therefore {\text{Rate}} = 10\% \cr} $$