Let the work be completed in *n* days when 4 workers are dropped on every day except on the first day.

Since 4 workers are dropped on every day except on the first day, total number of man days who worked for *n* days is the sum of *n* terms of an A.P. with first term as 150 and common difference as –4.

The work would have finished in (*n* − 8) days with 150 workers when the number of workers are not drooped.

Total number of man days who would have worked at all *n* days = 150(*n* – 8)

∴*n* (152 – 2*n*) = 150(*n* – 8)

⇒152*n* – 2*n* ^{2} = 150*n* – 1200

⇒ 2*n* ^{2} –2*n* – 1200 = 0

⇒* n* ^{2} – *n* – 600 = 0

⇒ (*n* – 25)(*n* + 24) = 0

⇒ *n* = 25 [*n* > 0]

Thus, the number days in which the work was to be completed is (25 – 8) = 17 days

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