Question

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

• A. $40$ months
• B. $60$ months
• C. $20$ months
• D. $30$ months

Answer 1

The correct option is C $20$ months

First month he pay $=20Rs.$
Second month he pays = $20+15$
Third month he pays = $20+2\times 15$
$nth$ month he pays = $20+(n-1)\times 15$
According to the question he increases his payment by $Rs.15$ every month.
Now, total payment paid by him = $\left(20\right)+(20+15)+(20+2\times 15)+...+20+(n-1)\times 15=3250$
$\Rightarrow 20n+15\times n\times \frac{(n-1)}{2}=3250$
$\Rightarrow 15n^2+25n-6500=0$
$\Rightarrow 3n^2+5n-1300$
$\Rightarrow n=\frac{120}{6},\frac{-130}{6}$
$\Rightarrow n=20$ and $-30$.
Hence, $n=20$.