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

Given:

A man saved Rs. 16500 in ten years. In each year after the first he saved Rs. 100 more than he did in the preceding year. 
To do:
We have to find the money he saved in the first year. 

Solution:

Let the amount saved in the first month be $x$.

Savings raised each successive year $=Rs.\ 100$

Amount saved each year for 10 successive years (in Rupees) is,

$x, x+100, x+200, ......$(10 terms)

This is in A.P., where

First term $a = x$

Common difference $d = 100$

Number of terms $n = 10$

We know that,

Sum of $n$ terms in an A.P. $S_n = \frac{n}{2}[2a + (n – 1) d]$

$S_n = \frac{10}{2}[2 (x) + (10 – 1) 100]$

$ 16500= 5[2x + 900]$

$3300 = 2x+900$

$2x=3300-900$

$2x=2400$

$x=1200$

Therefore, he saved Rs. 1200 in the first year.

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Updated on: 10-Oct-2022

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