On a certain sum of money the compound interest for 2 years is Rs 282.15 and the simple interest for the same period of time is Rs 270. The rate of interest per annum is = ?

Explanation:-

$$\eqalign{ & {\text{CI for 2 years}}\,{\text{ = Rs 282}}{\text{.15}} \cr & {\text{SI for 2 year}}\,{\text{ = Rs 270}} \cr & {\text{SI for 1 year = }}\frac{{270}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}\,135 \cr & {\text{Difference between CI and SI}} \cr & {\text{ = }}\left( {282.15 - 270} \right) \cr & {\text{ = Rs 12}}{\text{.15}} \cr & {\text{Required rate % }} \cr & {\text{ = }}\frac{{12.15}}{{135}} \times 100 = 9\% \cr}$$ Note : Always remainder for first year CI and SI will be same.