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

Given: -


Initially let the work can be completed in ndays when 150 workers work on every day.


However every day 4 workers are being dropped from the work so that work took 8 more days to be finished.


Finally, it takes (n + 8) days to finish the works.


Work equivalent when 150 workers work without being dropped = 150×n


Work equivalent when workers are dropped day by day = 150 + (150 - 4) + (150 - 8) + ...... + (150 - 4(n + 8)).


So,


150×n = 150 + (150 - 4) + ........ + (150 - 4×(n + 8))


150×n = 150×n + 150×8 - 4×(1 + 2 + 3 + ...... + (n + 8))


(n + 8)(n + 9) = 600


n2 + 17n - 528 = 0


n = - 33 or n = 16


Since the number of days cannot be negative, n = 16.


∴ In 24 days the work is completed.


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