Question

A contractor employed 150 workers to complete a job in a certain number of days due to the partial payment of wages every 4 day 4 more workers started dropping it took 8 more days to complete the job in how many days the job was completed

Answer 1

workers dropped from second day.

Let total days be 'N'.

Total work done = 150*N (man days)

Work done on first day = 150*1 = 150 (man days)

Work done by using 146 workers on second day = 146 man days

and so on.. for (N+8) days.

So 150*N = 150 + 146 + 142 + .....(N+8) terms........... + (150 - 4(N+8-1)) ..{A . P.}

150*N = 150(N+8) - {0 + 4 + 8 + 12 + .......   + 4(N+7)}

The bold region is in A. P. which has sum = (N+8)(4(N+7))/2

So

150*8 = 2(N+7)*(N+8) => N = 17, -32.

Actual expected days is 17 days but it is done in 25 days at dropping 4 on each