A sum of money becomes Rs. 20925 in 2 years and Rs. 24412.50 in 5 years. Find the rate of interest and the sum of money.

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {24412.50 - 20925} \right) \cr & = {\text{Rs}}{\text{. }}3487.50 \cr & {\text{S}}{\text{.I}}{\text{. }}{\text{for 2 years}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{3487.50}}{3} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}2325 \cr & \therefore \text{Principal} \cr & = {\text{Rs}}{\text{.}}\left( {20925 - 2325} \right) \cr & = {\text{Rs}}{\text{. }}18600 \cr & {\text{Hence,}} \cr & {\text{rate}} = \left( {\frac{{100 - 2325}}{{18600 \times 2}}} \right)\% \cr & = 6.25\% \cr} $$