Question : The simple interest on a sum of money is $\frac{8}{25}$ of the sum. If the number of years is numerically half of the rate percent per annum, then the rate percent per annum is:
Option 1: $5$%
Option 2: $8$%
Option 3: $6\frac{1}{4}$%
Option 4: $4$%
Correct Answer: $8$%
Solution :
Let Principal = $P$
$\therefore$ Simple Interest = $\frac{8}{25}P$
Let Rate = R% per annum
$\therefore$ Time = $\frac{R}{2}$ years
Rate = $\frac{SI \times 100}{\text{Principal}\times \text{Time}}$
⇒ R = $\frac{\frac{8}{25}P \times 100}{P\times \frac{R}{2}}$
⇒ R
2
= $\frac{8 \times 200}{25} = 64$
⇒ R = $\sqrt{64} = 8$% per annum
Hence, the correct answer is $8$%.
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