Question

A man repays a loan of $₹65,000$ by paying $₹400$ in the first month and then increasing the payment by $₹300$ every month. How long will it take for him to clear the loan?

• A. $24$ months
• B. $24$ months
• C. $20$ months
• D. $12$ months

Answer 1

The correct option is C $20$ months

Given, Loan amount $=₹65,000$

Repayment through installments $400+700+1000+1300+......$


So this series is in A.P. with $a=400$ , $d=300$ and $S_n=65000$

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

$\Rightarrow$ $\frac{n}{2}(2\times 400+(n-1\left)300\right)=65000$

$\Rightarrow$ $n(500+300n)=13000$

$\Rightarrow$ $300n^2+500n-13000=0$

$\Rightarrow$ $3n^2+5n-130=0$

$\Rightarrow$ $3n^2+65n-60n-130=0$

$\Rightarrow$ $(3n+65)(n-20)=0$

$\Rightarrow$ $n=20$ (As $n$ cannot be a fractional value)

Therefore he will take $20$ months to clear the loans.