Question

A contractor employed 150 workers to complete a job in a certain number of days. Due to partly payment of wages, every day 4 more workers start dropping. It took 8 more days to cotnplete the job. In how many days, the job was completed ?

Answer 1

Suppose the work is completed in n days.

4 workers dropped every day, except the 1st day.

Thus, the total number of workers who worked all n days is the sum of n terms of an A.P. with first term 150 and common difference -4.

$i.e.,\frac{n}{2}[2\times 150+(n-1\left)\right(-4\left)\right]$

$i.e.,n(152-2n)$

If the workers not dropped, then the work would finish in (n-8) days with 150 workers.

Workers who worked all n days = 150(n-8)

$n(152-2n)=150(n-8)$

$n^2-n-600=0$

$n^2-25n+24n+600=0$

$(n-25)(n+24)=0$

Since, number of days cannot be negative, therefore, n=25

Hence, the work is completed in 25 days.