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 x be the number of days in which 150 workers finish the work.

According to the given information,

150x = 150 + 146 + 142 + … (x + 8) terms

The series 150 + 146 + 142 + … (x + 8) terms is an A.P. with first term 150, common difference −4, and number of terms (x + 8).

∴ 150x = [(x + 8)/2][2(150) + (x + 8 − 1)(−4)]

⇒ 150x = (x + 8)[150 − 2(x + 7)]

⇒ 150x = (x + 8)(136 − 2x)

⇒ 75x = (x + 8)(68 − x)

⇒ 75x = 68x − x² + 544 − 8x

⇒ x² + 75x − 60x − 544 = 0

⇒ x² + 15x − 544 = 0

⇒ (x − 17)(x + 32) = 0

⇒ x = 17 or x = −32

Since x cannot be negative, x = 17.

Therefore, originally, the number of days in which the work was completed is 17.

Thus, required number of days = 17 + 8 = 25.