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?

Answer 1

Let the man save Rs. 200 in n numbers of years.

Then,

ATQ

32 + 36 + 40 + .... = 200

It forms a series of n terms, with a = 32 and d = 4

$\therefore S_n=\frac{n}{2}[2a+(n-1\left)4\right]$

$\Rightarrow 200=\frac{n}{2}\left[2\right(32)+(n-1\left)4\right]$

$\Rightarrow 400=60n+4n^2$

$\Rightarrow n^2+15n-100=0$

$\Rightarrow n=5$ or $-20$

But, $n\ne -20$ [It can't be negative]

$\therefore n=5$

The man will save Rs. 200 in 5 years.