Question : The Simple Interest on a sum of money is $\frac{1}{4}$ of the principal, and the number of years is equal to the rate percent per annum. The rate percent is:
Option 1: 2.5%
Option 2: 5%
Option 3: 7.5%
Option 4: 10%
Correct Answer: 5%
Solution :
Let the rate and time be $x$.
Given: SI = $\frac{1}{4}P$
By using the formula of Simple Interest: SI = $\frac{\text{P×R×T}}{100}$ where $P$ is principal, $T$ is time in years and $R$ is the rate of interest per annum.
$\frac{1}{4}P$ = $\frac{P×x×x}{100}$
⇒ $x^2$ = $\frac{100}{4}$
⇒ $x^2$ = 25
⇒ $x$ = 5
Hence, the correct answer is 5%.
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