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Q.

In just 10 months, a man saved ₹ 33,000. After the first, he saved an additional ₹ 100 over the previous month. In the first month, how much money did he save?

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a

₹2,550

b

₹3,550

c

₹2,850

d

₹2,800

answer is C.

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Detailed Solution

Given that in each month after the first, he saved ₹100 more than he did in the previous month.
Let the money saved by the man in the first month be ₹a.
So, the money saved by the man every month is in AP with a common difference of ₹100. Therefore, d = 100
As the number of months, n = 10 and sum of money saved in 10 months,

S 10 = 33000

.
Formula used for sum of first term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Applying sum of n terms of an A.P. formula:

∴ S 10 = 102 [2 a + (10 − 1) × 100] ⇒ 33000 = 5 × (2 a + 900) ⇒ 6600 = 2 a + 900 ⇒ 2 a = 6600 − 900 ⇒ 2 a = 5700 ⇒ a = 57002 ⇒ a = 2850

Therefore, the money saved by the man in the first month is ₹2,850.
Hence, option (3) is correct.

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