Question

A man saved 32 rs during first year, 36 rs in second year and in this way. He increases his saving by rupees 4 every year. Find in what time his saving will be 200 rs

Answer 1

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Answer 2

Answer:

In 5 years a man saving will be ₹ 200.

Step-by-step explanation:

Given :  

In first year a man saved, a = ₹ 32

In second year a man saved , a2 = ₹ 36

Increase in savings, d = 36 - 32 = 4

His saving in 'n' years will be , Sn = 200  

Let 'n' be the number of years.

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

200 = n/2 [2 × 32 + (n– 1)4]

200 × 2 = n[64  + 4(n - 1)]

400 = n[64 + 4n - 4]

400 = n[60 + 4n]

400 = 4n[15 + n]

400/4  = 15n + n²

100 = 15n + n²

n² + 15n – 100 = 0

n² + 20n – 5n – 100 = 0

[By middle term splitting]

n (n + 20) – 5 (n + 20) = 0

(n – 5) (n + 20) = 0

(n – 5) = 0, n = 5 &  (n + 20) = 0, n = - 20

Number of years can never be negative. Therefore, n = 5

Hence, in 5 years a man saving will be ₹ 200.

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