With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is = ?

$$\eqalign{ & \frac{{{\text{Principal}}}}{{{\text{Amount}}}} = \frac{{4 \times 5}}{{5 \times 5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{{25}} \cr & {\text{After three year}} \cr & \frac{{\text{P}}}{{\text{A}}} = \frac{{5 \times 4}}{{7 \times 4}} \cr & \,\,\,\,\,\,\,\, = \frac{{20}}{{28}} \cr & {\text{In three year S}}{\text{.I}}{\text{.}} \cr & = 28x - 25x \cr & = 3x \cr & \text{So, the required interest will be} \cr & 3x = \frac{{20x \times {\text{R}} \times 3}}{{100}} \cr & {\text{R}} = 5\% \cr} $$