Simple interest on a certain sum one-fourth of the sum and the interest rate percentage per annum is 4 times the numbers of years. If the rate of interest increases by 2%, then what will be the simple interest (in Rs.) on Rs. 5,000 for 3 years?

\[\frac{1}{4}\begin{array}{*{20}{c}} {\,\,\,\, \leftarrow {\text{S}}{\text{.I}}{\text{.}}} \\ { \leftarrow P} \end{array}\]
$$\eqalign{ & {\text{Let }}P = 4x{\text{ and S}}{\text{.I}}{\text{.}} = x \cr & {\text{Time}} = t{\text{ years}} \cr & {\text{Rate}} = 4t\% \cr & \therefore {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times R \times T}}{{100}} \cr & x = \frac{{4x \times 4t \times t}}{{100}} \cr & {t^2} = \frac{{100}}{{16}} \cr & {t^2} = \frac{{25}}{4} \cr & \therefore t = \frac{5}{2} = 2.5{\text{ years}} \cr & \therefore R = 4 \times 2.5{\text{ years}} = 10\% \cr & {\text{New rate}} = 10\% + 2\% \cr & P = {\text{Rs}}{\text{. }}5000 \cr & T = 3{\text{ years}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times R \times T}}{{100}} \cr & = \frac{{5000 \times 12 \times 3}}{{100}} \cr & = {\text{Rs}}{\text{. }}1800 \cr} $$