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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.

Asked by Rishabh Sinha(student) , on 24/2/12

Answers

Let the work be completed inndays 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 forndays is the sum ofnterms of an A.P. with first term as 150 and common difference as –4.
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 allndays = 150(n– 8)
n(152 – 2n) = 150(n– 8)
⇒152n– 2n2= 150n– 1200
⇒ 2n2–2n– 1200 = 0
n2n– 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

Posted by Swetha Reddy(student)on 24/2/12

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