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.

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