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A man saved Rs. 66,000 in 20 years. In each succeeding year after the first year he saved Rs. 200 more than what he saved in the previous year. How much did he save in first year?

A man saved Rs. 66,000 in 20 years. In each succeeding year after the first year he saved Rs. 200 more than what he saved in the previous year. How much did he save in first year? Correct Answer Rs. 1,400

Given:

Total amount saved in 20 years = Rs. 66000

Each year saving is increased by Rs. 200

Formula Used:

Sn = n/2(2a + (n - 1 )d)

where n = number of terms

d = common difference 

a = first term

Calculation:

Let the amount saved in the first year be Rs. a

As saving of Rs. 200 is increased every year 

Common difference = 200 

Number of years = 20 

Now,

66000 = 20/2(2a + (20 - 1) 200)

⇒ 66000 = 10(2a + 19 × 200)

⇒ 66000 = 20a + 38000

⇒ 66000 - 38000 = 20a 

⇒ 2a = 28000

⇒ a = 1400

∴ Rs. 1400 was saved in the first year

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