Question

The simplest intrest on a certain sum is one fourth of the sum. If the number of years and the rate of annual interest are numerically equal then the number of year is. ​

Answer 1

Answer:

$let \: rate \: of \: annual \: interest \: and \: time \: be \: x$

$let \:the \: sum \: be \: y \\ s.i = \frac{y}{4}$

$\frac{y}{4} = \frac{y \times x \times x}{4 \times 100} \\ \frac{y}{4 \times y} = \frac{ {x}^{2} }{400} \\ \frac{1}{4} = \frac{ {x}^{2} }{400 } \\ {x}^{2} = \frac{400}{4} \\ x = \sqrt{100} = 10 \: years$