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A man saved Rs. $16500$ in ten years. In each year after the first he saved Rs. $100$ more than he did in the preceding year. How much did he save in the first year?

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Rs.

1400

Rs.

1600

Rs.

1500

Rs.

1200

answer is D.

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Detailed Solution

Given, a man saved Rs.

16500

in ten years. In each year after the first he saved Rs.

100

more than he did in the preceding year.
As we know the sum of the first n terms of an AP is given by

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

… (1)
According to the given condition, we have,

S_{n} = 16500, n = 10, d = 100

Putting these values in (1), we get,

16500 = \frac{10}{2} [2 a + (10 - 1) 100]

⇒

16500 = 5 [2 a + 900]

⇒

16500 = 10 a + 4500

⇒

10 a = 12000

⇒

a = 1200

Therefore, he saved Rs.

1200

in the first year.
Hence, the correct option is 4.

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