Question

Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

Answer 1

Clearly saving of Yasmeen forms an AP with first term $a=32$ and common difference $d=36-32=4$.
Let it take $n$ months to saves Rs. $2000$.
$\therefore S_n=\frac{n}{2}[2a+(n-1\left)d\right]=2000$
$\Rightarrow \frac{n}{2}[2\times 32+(n-1)\times 4]=2000$
$\Rightarrow n[2n+30]=2000$
$\Rightarrow n[n+15]=1000$
$\Rightarrow n^2+15n-1000=0$
$\Rightarrow (n+40)(n-25)=0$
$\Rightarrow n=-40,25$
But n=-40 being negative integer is not possible.
$\therefore n=25$
Hence, it takes 25 months for Yasmeen to saves Rs.2000.