Question

The simple interest on a certain sum of money at the given rate of interest is directly proportional to the period. The simple interest on a sum of money at same rate for 2 years is Rs. 175. Find the interest on the same sum with the same rate for 6 years.

Answer 1

$$\begin{gathered} \mathrm{Let}I\mathrm{denote}\mathrm{the}\mathrm{simple}\mathrm{interest}andT\mathrm{denote}\mathrm{the}\mathrm{time}\mathrm{period}. \\ I\alpha T\left(\mathrm{Given}\right) \\ I=KT(H\mathrm{ere},K\mathrm{is}a\mathrm{constant}.) \\ \mathrm{When}I=\mathrm{Rs}175andT=2\mathrm{years}, \\ 175=K\times 2 \\ \Rightarrow K=\frac{175}{2} \\ Now, \\ I=\frac{175}{2}T(E\mathrm{quation}\mathrm{of}\mathrm{variation}) \\ \therefore I=\frac{175}{2}\times 6(\because T=6\mathrm{years}) \\ =\mathrm{Rs}525 \end{gathered}$$