150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

Answer

25 days

Explanation

Suppose the work is completed in n days. Since 4 workers dropped every day except the first day, the total amount of work done in n days is the sum of n terms of an A.P. with first term 150 and common difference -4.
`therefore` Total amount of work done
`=n/2[2xx150+(n-1)xx(-4)]=n(152-2n)`
Had the workers not dropped, the work would have finished in (n-8) days with 150 workers working each day. Therefore, the total amount of work done in n days is 150 (n-8).
`therefore` n(152-2n)=150(n-8)
`rArrn^(2)-n-600=0`
`rArr(n-25)(n+24)=0`
`rArrn=25`
Thus, the work is completed in 25 days