Question

A man repays a loan of $₹3250$ by paying $₹20$ in the first month and then increases the payment by $₹15$ every month. How long will it take him to clear the loan?

Answer 1

Suppose the loan is cleared in $n$ months.

Clearly, the amounts form an A.P. with the first term $20$ and the common difference $15$.

and, the sum of the amounts $=3250$

$$\begin{gathered} ⟹\frac{n}{2}\left\{2\times 20+(n-1)\times 15\right\}=3250 \\ ⟹\frac{n}{2}\left\{40+15n-15\right\}=3250 \\ ⟹n(15n+25)=6500 \\ ⟹152n^2+25n-6500=0 \\ ⟹3n^2+5n-1300=0 \\ ⟹(n-20)(3n+65)=0 \end{gathered}$$

Either, $(n-20)=0$ or $(3n+65)=0$

$\Rightarrow n=20$ or $n=-15$

Since the number of months cant be negative.

So, $n=20$

Hence, the loan is cleared in $\mathbf{20}$ months.