150 workers were engaged to finish a piece of work in a

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150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed?

1. 28
2. 24
3. 25
4. 30

Correct Option: C

Let 150 workers complete the work in x days.
∴ 150 × x = 150 + 146 + .... to
(x + 8) terms
On putting x = 17
LHS = 150 × 17 = 2550
RHS = 150 + 146 + .... to 25 terms
a = 150, d = –4, n = 25

∴ S =	n	[2a + (n–1) d]
	2

=	25	[2 × 150 + 24 × (–4)]
	2

=	25	(300 – 96) =	25 × 204	= 2550
	2		2

Note : It is better to solve by options.