Question

A contractor employed 150 labourers to finish a peice of work in a certain no. of days. 4 workers went away the second day, 4 more workers went away the third day and so on. If it took 8 more days to finish the work , find the no. of days in which the work was completed. ANURAG.

Answer 1

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 – 2n) = 150(n – 8)
⇒152n – 2n 2 = 150n – 1200
⇒ 2n 2 –2n – 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