If a sum of money becomes Rs. 4000 in 2 years and Rs. 5500 in 4 years 6 months at the same rate of simple interest per annum. Then the rate of simple interest is = ?

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. of 2}}{\text{.5 years}} \cr & {\text{ = 5500}} - {\text{4000}} \cr & {\text{ = 1500}} \cr & {\text{S}}{\text{.I}}{\text{. of 2 years}} \cr & {\text{ = }}\frac{{1500}}{{2.5}} \times {\text{2}} \cr & {\text{ = 1200}} \cr & {\text{So, Principal}} \cr & {\text{ = 4000}} - {\text{SI of 2 years}} \cr & \Rightarrow {\text{Principal = 4000}} - 1200 \cr & \Rightarrow {\text{Principal = 2800}} \cr & {\text{r}}\% {\text{ = }}\frac{{1200}}{{2800 \times 2}} \times {\text{100}} \cr & \,\,\,\,\,\,\,\,{\text{ = 21}}\frac{3}{7}\% \cr} $$