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 n days 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
n^2 + 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.