# 150 Workers Were Engaged To Finish Piece Of Work In Certain No Of Days

150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d … number. of days in which the work…

Suppose the work is completed in n days.

Since 4 workers went away on every day except the first day.

∴ Total number of worker who worked all the n days is the sum of n terms of A.P. with first term 150 and common difference – 4.

Total number of worker who worked all the n days If the workers would not have went away, then the work would have finished in (n – 8) days with 150 workers working on every day.

∴ Total number of workers who would have worked all n days = 150 (n – 8)

n (152 – 2n) = 150 (n – 8)

⇒ 152n – 2n2 = 150n – 1200

⇒ 2n2 – 2n – 1200 = 0

n2n – 600 = 0

n2 – 25n + 24n – 600 = 0

n(n – 25) + 24 (n + 25) = 0

⇒ (n – 25) (n + 24) = 0

n – 25 = 0 or n + 24 = 0

n = 25 or n = – 24

n = 25  ( Number of days cannot be negative)

Thus, the work is completed in 25 days.