150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more 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.

Asked by preeti18 | 29th Nov, 2010, 05:10: PM

Expert Answer:

Dear student
Let the initialy the work was to be completed in x days with 150 workers working on it
But every day 4 workers are being dropped from the work hence
work took 8 more days to be finished so x+8 days are taken to finish it
So the work is of 150x man days
i.e 150x =150+(150-4)+(150-8)+(150-12)+......+(150-4(x+8))
150x=150x+150x8-4(1+2+3+....+(x+8)terms)
So, 600=(x+8)(x+9)
or x2+17x-528=0
or x = -33 or 16
No. of days must be positive so x = 16
So the work took 24 days in the revised arrangement
Regards
Team Topper

Answered by  | 30th Nov, 2010, 10:12: AM

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