150 workers were engaged to finish a job in a certain number of days

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.

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 150 x man days
i.e 150 x =150 + (150-4) + (150-8) + (150-12) + …+ (150 - 4(x + 8))
150 x = 150 x+150 x8-4(1 + 2 + 3 +… + (x + 8)terms)
So, 600 = (x + 8)(x + 9)
or x 2 + 17 x - 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