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 =Rs 100

Number of months, n = 10

Sum of money saved in 10 months, s₁₀ = ₹ 33,000 

`"Using the formula ," S_n = n/2 [2a + (n-1) d],`we get

`S_10 = 10/2 [2a + (10-1) xx 100 ] = 33000`

⇒  5 (2a +900 )= 33000

⇒ 2a +900=6600

⇒ 2a = 6600-900=5700

⇒ a = 2850

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