Question : The simple interest on a sum of money is $\frac {1}{16}$th of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:
Option 1: $1\frac{1}{2}$%
Option 2: $2\frac{1}{2}$%
Option 3: $3\frac{1}{2}$%
Option 4: $4\frac{1}{2}$%
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Correct Answer: $2\frac{1}{2}$%
Solution :
We know, Simple Interest =$\frac{\text{Principal×Rate×Time}}{100}$
Let the number of years and rate be $r$ and the sum be $x$.
So, according to the given conditions,
$\frac{x}{16}=\frac{x×r×r}{100}$
$⇒r^2=\frac{100}{16}$
$\therefore r = \frac{10}{4}=2\frac{1}{2}$%
Hence, the correct answer is $2\frac{1}{2}$%.
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