Question

A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?

Answer 1

Let the money saved by the man in the first month be ₹a.

It is given that in each month after the first, he saved ₹100 more than he did in the preceding month. So, the money saved by the man every month is in AP with common difference ₹100.

∴ d = ₹100

Number of months, n = 10

Sum of money saved in 10 months, S₁₀ = ₹33,000

Using the formula, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$, we get

$$\begin{gathered} S_{10}=\frac{10}{2}\left[2a+\left(10-1\right)\times 100\right]=33000 \\ \Rightarrow 5\left(2a+900\right)=33000 \\ \Rightarrow 2a+900=6600 \\ \Rightarrow 2a=6600-900=5700 \end{gathered}$$
$\Rightarrow a=2850$

Hence, the money saved by the man in the first month is ₹2,850.