Question

Tulsiram borrowed some money from a bank for $2\frac{1}{2}$years at the rate of 10% per annum. To repay his debt he had to pay Rs 10,250 as interest. What was the principal that he had borrowed?

Answer 1

Time (N) = $2\frac{1}{2}\mathrm{years}=\frac{5}{2}\mathrm{years}$
Rate (R) = 10%
Interest = I = Rs 10,250
We have $\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100}$
$$\begin{gathered} \Rightarrow 10250=\frac{\mathrm{P}\times 10\times {\displaystyle \frac{5}{2}}}{100} \\ \Rightarrow 10250=\frac{\mathrm{P}\times 5\times 5}{100} \\ \Rightarrow 10250=\frac{\mathrm{P}\times 25}{100} \end{gathered}$$

On multiplying both sides with 100, we obtain:
$$\begin{gathered} 10250\times 100=\frac{\mathrm{P}\times 25}{100}\times 100 \\ \Rightarrow 1025000=\mathrm{P}\times 25 \end{gathered}$$
On dividing both sides by 25, we obtain:
$$\begin{gathered} \frac{1025000}{25}=\frac{\mathrm{P}\times 25}{25} \\ \Rightarrow 41000=\mathrm{P} \\ \mathrm{Therefore},\mathrm{principal}=\mathrm{Rs}41000 \end{gathered}$$