Question

A man saves ₹ 32 during the first year, ₹ 36 in the second year and in this way he increases his savings by ₹4 every year. Find in what time his saving will be ₹200.

Answer 1

Given : A man saves Rs. 32 during first year and increases his savings by Rs. 4 every year. His total saving is Rs. 200 

To find : Time taken in years by him to save Rs. 200. 

A man saves in the first year is 32Rs 

He saves in the second year is 36Rs. 

In this process he increases his savings by Rs. 4 every year 

Therefore, 

A.P. will be 32, 36, 40,………………… 

Where 32 is first term and common difference, 

d = 36 – 32 = 4 

We know, 

S_n is the sum of n terms of an A.P

Formula used :

S_n = \(\frac{n}{2}\){2a + (n-1)d}

Where a is first term, d is common difference and n is number of terms in an A.P. 

According to the question :

S_n = 200

Therefore,

n can not be a negative values as days can not hold negative values 

⇒ n = 5 

Hence, he has to do saving for 5 days to save Rs. 200.