A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

Solution(By Examveda Team)

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\kern 1pt} {\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {12005 - 9800} \right) \cr & = {\text{Rs}}{\text{. }}2205 \cr & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{2205}}{3} \times 5} \right) \cr & = {\text{Rs}}{\text{.}}\,3675 \cr & \therefore {\text{Principal}} \cr & = {\text{Rs}}{\text{.}}\,(9800 - 3675) \cr & = {\text{Rs}}{\text{.}}\,6125 \cr & {\text{Hence,}}\,{\text{rate}} = \left( {\frac{{100 \times 3675}}{{6125 \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$