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