$40$ men can finish a work in $60$ days. After they work for $20$ days, $20$ more men join them. The total…

$40$ men can finish a work in $60$ days. After they work for $20$ days, $20$ more men join them. The total time from start in which the work is completed is:
  1. $40$ days
  2. $\dfrac{140}{3}$ days
  3. $48$ days
  4. $50$ days

Solution

Total work $= 40 \times 60 = 2400$ man-days. In $20$ days, work done $= 800$. Remaining $= 1600$ man-days. With $60$ men: $\dfrac{1600}{60} = \dfrac{80}{3}$ more days. Total $= 20 + \dfrac{80}{3} = \dfrac{60 + 80}{3} = \dfrac{140}{3}$ days.

Asked in: IMO

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