Question

Find the time in which the simple interest at $2\%$p.a on a sum of money is ${\frac{1}{25}}^{\mathrm{th}}$ of the principal.

Answer 1

Let Principal $=₨\mathrm{P}$

Given:

Simple interest $=\frac{1}{25}\times \mathrm{P}=\frac{\mathrm{P}}{25}$

Rate of Interest $=2\%$ p.a

Let Time$=\mathrm{T}$years

We know that

Simple interest $=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}$

Then,

$\frac{\mathrm{P}}{25}=\frac{\mathrm{P}\times 2\times \mathrm{T}}{100}$
$$\begin{gathered} \Rightarrow \mathrm{T}=\frac{{\displaystyle \frac{\mathrm{P}}{25}\times 100}}{\mathrm{P}\times 2} \\ \Rightarrow \mathrm{T}=\frac{4}{2} \\ \Rightarrow \mathrm{T}=2 \end{gathered}$$

Hence, the required time is $2$ years.