Question:
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
Solution:
Let n be the time in which the man saved Rs 200.
Here, d= 4, a = 32
We know:
$S_{n}=\frac{n}{2}\{2 a+(n-1) d\}$
$\Rightarrow 200=\frac{n}{2}\{2 \times 32+(n-1) 4\}$
$\Rightarrow 400=64 n+4 n^{2}-4 n$
$\Rightarrow 4 n^{2}+60 n-400=0$
$\Rightarrow n^{2}+15 n-100=0$
$\Rightarrow n^{2}+20 n-5 n-100=0$
$\Rightarrow(n+20)(n-5)=0$
$\Rightarrow n=5, n=-20 \quad$ (Rejecting the negative value)
Therefore, the man took 5 years to save Rs 200.