Question : The simple interest received on a sum is $\frac{25}{36}$ of the sum. The number of years is equal to the annual rate of interest. What is the annual rate of interest?
Option 1: 9.25 percent
Option 2: 10.25 percent
Option 3: 6.62 percent
Option 4: 8.33 percent
Correct Answer: 8.33 percent
Solution :
Rate of interest = $r$
Time = $r$
Let the sum value be $x$, then Simple Interest will be:
Simple Interest = $\frac{(x \times r \times r)}{100}$
⇒ $(\frac{25}{36})x = \frac{(x \times R^2)}{100}$
⇒ $(\frac{25}{36}) = \frac{(r^2)}{100}$
⇒ $r^2 = (\frac{25 \times 100}{36})$
⇒ $r^2 = (\frac{25 \times 100}{36})$
⇒ $r^2 = \frac{50}{6}$
⇒ $r = 8.33$%
So, the annual rate of interest is 8.33%.
Hence, the correct answer is 8.33 percent.
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