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