Certain number of men can complete a work in 16 days. They start working together. Starting from second day a man leaves at the start of the day. The work now gets completed at the end of the day when the last person works. How many men were there at the start.
Explanation:
Let the number of men at the start be ‘m’.
Let efficiency of each man be 1 unit/day.
When all of them work it takes 16 days to complete the work.
∴ Total work done = m × 16 units.
Now, if a person leaves at the start of every day.
Work done on 1st day = m × 1 = m units
Work done on 2nd day = (m – 1) × 1 = (m – 1) units . . . Work done on mth day = 1 × 1 = 1 units
∴ Total work done = m + (m – 1) + … + 1 = m(m + 1)/2 units.
⇒ m(m + 1)/2 = m × 16
⇒ m = 31
Hence, 31.
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