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Question

150 workers were engaged to finish a job in a certain number of days.4 workers dropped out on second day, 4more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

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Solution

Let x be the number of days in which 150 workers finish the work.
According to the given information,
150x=150+146+142+...(x+8)terms
The series 150+146+142+...+(x+8) terms is an A.P. with first term 150, common difference -4 and number of terms as (x+8)
150x=x+82[2(150)+(x+81)(4)]
150x=(x+8)[(150)+(x+7)(2)]150x=(x+8)(1502x14)
150x=(x+8)(1362x)
75x=(x+8)(68x)
75x=68xx2+5448x
x2+75x60x544=0
x2+15x544=0
x2+32x17x544=0
x+(x+32)17(x+32)=0
(x17)(x+32)=0
x=17 or x=32
Since, x cannot be negative . So, x=17
So, the number of days in which the work was to be completed by 150 workers is 17.
So, required number of days =(17+8)=25

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