Question

In how much time will a sum of money triple itself at$25\%$ per annum?

Answer 1

Let Principal $=₨\mathrm{P}$

Given: Amount $=₨3\mathrm{P}$

Rate of Interest $=25\%$ p.a

Let Time$=\mathrm{T}$years

Since, Amount $=$ Principal $+$ Simple Interest

$$\begin{gathered} \Rightarrow 3\mathrm{P}=\mathrm{P}+\mathrm{SI} \\ \Rightarrow \mathrm{SI}=3\mathrm{P}-\mathrm{P} \\ \Rightarrow \mathrm{SI}=2\mathrm{P} \end{gathered}$$

We know that

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

Then,

$2\mathrm{P}=\frac{\mathrm{P}\times 25\times \mathrm{T}}{100}$
$$\begin{gathered} \Rightarrow \mathrm{T}=\frac{2\mathrm{P}\times 100}{\mathrm{P}\times 25} \\ \Rightarrow \mathrm{T}=2\times 4 \\ \Rightarrow \mathrm{T}=8 \end{gathered}$$

Hence, the required time is $8$ years.