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Q.

A man saves Rs. 200 in each of the firs! three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. After how many months his total savings from the start of service will be Rs. 11040

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a

18 months

b

19 months

c

201nonths

d

21 months

answer is D.

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Detailed Solution

Let the total saving after $n$ months of service be $₹ 11040 .$ Then,

$\begin{array}{l} 200 + 200 + 200 + 240 + 280 + \dots to n terms = 11040 \\ \Rightarrow 400 + \frac{n - 2}{2} {400 + (n - 3) \times 40} = 11040 \\ \Rightarrow (n - 2) (20 n + 140) = 10640 \\ \Rightarrow (n - 2) (n + 7) = 532 \\ \Rightarrow n^{2} + 5 n - 546 = 0 \\ \Rightarrow (n + 26) (n - 21) = 0 \\ \Rightarrow n = 21 \end{array}$

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A man saves Rs. 200 in each of the firs! three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. After how many months his total savings from the start of service will be Rs. 11040