Question

Aman saved Rs.32 during the first year, Rs.36 in the second year and in this way he increases his savings by Rs.4 every year. Find in what time his saving will be Rs.200.

Answer 1

Given, 

A man saved in first year, a = 32

A man saved in second year, a₂ = 36 

Increase saving, d = 4 

In n years his saving will be 200, S_n = 200 

We know, S_n =\(\frac{n}{2}\) [2a + (n – 1) d] 

200 = \(\frac{n}{2}\)[2(32) + (n – 1) 4] 

400 = n [64 + 4n – 4] 

400 = n [60 + 4n] 

400 = 4n [15 + n] 

100 = 15n + n² 

n² + 15n – 100 = 0

n² + 20n – 5n – 100 = 0 

n (n + 20) – 5 (n + 20) = 0 

(n – 5) (n + 20) = 0 

Here, n – 5 = 0, n = 5 

n + 20 = 0, 

n = -20 

The term can never be negative. So, we consider n = 5 

Hence, in 5 years his saving will be Rs. 200