Question

Question 35
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

Given that,
Yasmeen, during the first month, saves = Rs. 32
During the second month, saves = Rs. 36
During the third month, saves = Rs. 40
Let Yasmeen saves Rs. 2000 in "n" months.
Here, we have an arithmetic progression 32, 36, 40……
First term (a) = 32, common difference (d) = 36 - 32 = 4
$S_n$ = Rs. 2000
We know that, sum of first n terms of an AP is,
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow 2000=\frac{n}{2}[2\times 32+(n-1)\times 4]$
$\Rightarrow 2000=n(32+2n-2)$
$\Rightarrow 2000=n(30+2n)$
$\Rightarrow 1000=n(15+n)$
$\Rightarrow 1000=15n+n^2$
$\Rightarrow n^2+15n-1000=0$
$\Rightarrow n^2+40n-25n-1000=0$
$\Rightarrow n(n+40)-25(n+40)=0\Rightarrow (n+40)(n-25)=0$
$\therefore n=25[\because n\ne -40]$
Hence, she will save Rs. $2000$ in $25$ months.