Question

A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?

Answer 1

As, in each succeeding year after the first year he saved ₹200 more than what he saved in the previous year.
So, the savings of each year are in A.P.

We have,
the total savings of the man in 20 years, S₂₀ = ₹66000 and
the difference of his savings in each succeeding year, d = ₹200

Let his savings in the first year be a.

Now,
$$\begin{gathered} S_{20}=66000 \\ \Rightarrow \frac{20}{2}\left[2a+\left(20-1\right)d\right]=66000 \\ \Rightarrow 10\left[2a+19\times 200\right]=66000 \\ \Rightarrow 2a+3800=\frac{66000}{10} \\ \Rightarrow 2a=6600-3800 \\ \Rightarrow a=\frac{2800}{2} \\ \therefore a=1400 \end{gathered}$$

So, he saved ₹1400 in the first year.