Question

150 workers were engaged to finish a piece of work in certain number of days. Four workers dropped the second day, four 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 1

Step-by-step explanation:

let the work be complete in x days

The work should have been complete by x-8 days.

Total man-days= 150(x-8)

As four worker drop on each day

The total work days are 150,150-4, 150-8..... 150-(x-1)4

These are in arithmetic progression where

                           a1=150  d= - 4 and n=x

so total working man-days= x(2a1-4(x-1))/2

x(300-4x+4)/2

Then we have 150(x-8)=x(304-4x)/2

⇒ 300x-2400= 304x-4x²

⇒ 75x-600=76x-x²

⇒ x² -x -600=0

⇒ (x-25)(x+24)=0

solving we have x=25

The work was complete in 25 days.