150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the no. of days in which the work was completed.
Let the work be completed in n days when 4 workers are dropped on every day except on the first day.
Since 4 workers are dropped on every day except on the first day, total number of man days who worked for ndays is the sum of n terms of an A.P. with first term as 150 and common difference as –4.
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The work would have finished in (n − 8) days with 150 workers when the number of workers are not drooped.
Total number of man days who would have worked at all n days = 150(n – 8)
∴n (152 – 2n) = 150(n – 8)
⇒152n – 2n 2 = 150n – 1200
⇒ 2n 2 –2n – 1200 = 0
⇒ n 2 – n – 600 = 0
⇒ (n – 25)(n + 24) = 0
⇒ n = 25 [n > 0]
Thus, the number days in which the work was to be completed is (25 – 8) = 17 days
