Prerna saves ₹ $\displaystyle 32$ during the first month, ₹ $\displaystyle 36$ in the second month and ₹ $\displaystyle 40$ in the third month. If she continues to save in this manner, in how many months will she save ₹ $\displaystyle 2,000$ ?

ATQ, \[\begin{aligned} & 32+36+40+\ldots . .=2,000 \\ & a=32, d=4 \end{aligned} \] Let 'n' be the number of months. \[\begin{aligned} & S_{n}=2000 \\ & \frac{n}{2}[2(32)+(n-1) 4]=2000 \\ & n^{2}+15 n-1000=0 \\ & n^{2}+40 n-25 n-1000=0 \\ & (n+40)(n-25)=0 \\ & \Rightarrow n=-40, n=25 \end{aligned} \] (rejecting) \[\therefore \mathrm{n}=25 \] So, Prerna will save ₹ $\displaystyle 2,000$, in $\displaystyle 25$ months.