Question

The simple interest on a sum of money is 8 25 of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annum is

Answer 1

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Answer 2

Rate of interest per annum is 8%  

Given:  

Simple Interest $=\frac{8}{25}(\mathrm{P})$

Number of years $\mathrm{N}=\frac{R}{2}$

To find:

The rate percent per annum.

Solution:

By formula, Simple Interest $=\frac{P N R}{100}$, where P – principal, N – number of years, R – rate of interest

Given Simple Interest $=\frac{8}{25} \times P$

Number of years $=\frac{R}{2}$

In formula, Simple Interest $=\frac{P N R}{100}$, substituting the above terms in the equation becomes,  

$\frac{8}{25} \times P=\frac{P R R}{2 \times 100}$

$\frac{8}{25}=\frac{R R}{2 \times 100}$

$\frac{8}{25}=\frac{R^{2}}{2 \times 100}$

$\frac{2 \times 100 \times 8}{25}=R^{2}$

$\begin{array}{l}{2 \times 4 \times 8 \times=R^{2}} \\ {64=R^{2}} \\ {R=8}\end{array}$

The rate of interest per annum for the given simple interest is 8 %.