40 persons begin to work together on a job. But after some days 10 persons left the work. As a result, the job which should have been completed in 50 days is completed in 60 days. How many days after the commencement of the work did the 10 persons leave?
20
Total work \(= 40 \times 50 = 2000\) person-days.
Let the 10 persons leave after \(x\) days. For the first \(x\) days all 40 persons work, and for the remaining \(60 - x\) days only \(40 - 10 = 30\) persons work.
So the work done is \(40x + 30(60 - x) = 2000\).
Expand: \(40x + 1800 - 30x = 2000\), which gives \(10x = 200\).
Therefore \(x = 20\).
Hence, the 10 persons left 20 days after the commencement of the work.
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