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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:

a) 5%
b) 8%
c) 12%
d) 15%

Answer: c
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\kern 1pt} {\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {12005 – 9800} \right) \cr & = {\text{Rs}}{\text{. }}2205 \cr & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{2205}}{3} \times 5} \right) \cr & = {\text{Rs}}{\text{.}}\,3675 \cr & {\text{Principal}} = {\text{Rs}}{\text{.}}\,(9800 – 3675) \cr & = {\text{Rs}}{\text{.}}\,6125 \cr & {\text{Rate}} = \left( {\frac{{100 \times 3675}}{{6125 \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$

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