The simple interest on a certain sum is one-eighth of the sum when the number of years is equal to half of the rate percentage per annum. Find the simple interest (in Rs.) on Rs. 15,000 at the same rate of simple interest for 8 years.

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let sum}} = P \cr & \frac{{P \times r \times t}}{{100}} = \frac{1}{8}P \cr & rt = \frac{{100}}{8} = \frac{{25}}{2}\,.....\,\left( {\text{i}} \right) \cr & {\text{Since }}t = \frac{r}{2} \cr & {\text{From equation}}\left( {\text{i}} \right) \cr & r \times \frac{r}{2} = \frac{{25}}{2} \cr & r = 5\% \cr & {\text{If }}P = 1500 \cr & t = 8{\text{ years}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times r \times t}}{{100}} \cr & = \frac{{15000 \times 8 \times 5}}{{100}} \cr & = {\text{Rs}}{\text{. }}6,000 \cr} $$