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 have in the first month?

Answer 1

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

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

Therefore,d=100

Number of month, n = 10

Total sum of money saved in 10 months, $S_{10}=Rs.33,000$

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

$S_{10}=\frac{10}{2}[2\times a+(10–1)\times 100]=33000$

$=5\times (2a+900)=33000$

⇒$2a+900=6600$

⇒$2a=6600–900=5700$

⇒$a=2850$

Hence, the money saved by the man in the first months is Rs. 2850.