Question

Find the time in which the simple interest on a sum of money will be $0.125$ times the principal at $10\%$ p.a.

Answer 1

Let principal $=₨\mathrm{P}$

Given:

Simple interest $=0.125\times \mathrm{P}=0.125\mathrm{P}$

rate of interest $=10\%$p.a.

Let time $=\text{T}$ years.

We know that

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

Then,

$0.125\mathrm{P}=\frac{\mathrm{P}\times 10\times \mathrm{T}}{100}$
$$\begin{gathered} \Rightarrow \mathrm{T}=\frac{0.125\mathrm{P}\times 100}{\mathrm{P}\times 10} \\ \Rightarrow \mathrm{T}=\frac{125\times 100}{1000\times 10} \\ \Rightarrow \mathrm{T}=\frac{125}{100} \\ \Rightarrow \mathrm{T}=\frac{5}{4} \\ \Rightarrow \mathrm{T}=1.25 \end{gathered}$$

Hence, the required time is $1.25$ years or $1$year $3$months.