Question

A man saved Rs. 16500 in ten years. In each year after the first he saved Rs. 100 more than he did in the receding year. How much did he save in the first year?

Answer 1

Let the amount saved by the man in first year be x.

Then,

ATQ

$x+(x+100)+(x+200)+\dots \dots +(x+900)$

$=16500$

As his saving increased by Rs. 100 every year,

$\therefore 10x+100+200+\dots \dots +900=16500\dots \dots \left(i\right)$

Here,

100 + 200 + 300 + .... + 900 form a series of a = 100, d = 100 and n = 9

So, $S_n=\frac{n}{2}[a+l]$

$S_9=\frac{9}{2}[100+900]=4500\dots \dots \left(ii\right)$

From (i) and (ii)

$10x+\left(4500\right)=16500$

$10x=12000$

Or $x=1200$

The man saved Rs. 1200 in the first year.