Question

A man saved Rs.16500 in ten years . In each year after the first, he saved Rs.100 more than what he did in the preceding year. How much did he save in the first year?
A. Rs 1400
B. Rs.1600
C. Rs.1500
D. Rs.1200

Answer 1

Hint- From the given question we can easily find out it is in arithmetic progression, So using the formula of sum of n terms of an AP, solve it.

Complete step-by-step answer:
It is given that a man total of Rs.16,500 in a span of 10 years
Also, it is given that a man uniformly increases his savings by Rs.100 after every year
So, we can say that the progression is in Arithmetic Progression
It is given that the total amount he saved in 10 years =Rs.16,500
So, from the given data we can write
${S_{10}} = 16,500$ ,n=10, d=100(Since the amount is increasing uniformly by 100 after every year),we have to find out the savings in the first year that is a=?
We know that sum to n terms of an AP is given by
${S_n} = \dfrac{n}{2}[2a + (n - 1)d]$
$\Rightarrow {S_{10}} = \dfrac{{10}}{2}[2a + (10 - 1)100] \\\ \Rightarrow 16500 = 5[2a + 900] \\\ \Rightarrow 16500 = 10a + 4500 \\\$
From this, we get
10a=16500-4500
10a=12000
Therefore, the value of a=1200
So, the savings of the man in the first year=a=Rs.1,200

Note: If the last installment of savings of the man was given, we can make use of the formula of the Gaussian method and solve it.