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150 workers were engaged to finish a piece of work in certain no of days. four workers drop the second day . four more workers drop the third day and so on

. it took 8 more days to finish the work then find the no of days in which the work was completed?

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.