$8$ men can complete a piece of work in $24$ days. After $6$ days, $4$ more men join. The remaining work is…

$8$ men can complete a piece of work in $24$ days. After $6$ days, $4$ more men join. The remaining work is done in:
  1. $10$ days
  2. $12$ days
  3. $14$ days
  4. $15$ days

Solution

Total work $= 8 \times 24 = 192$ man-days. In $6$ days, work done $= 8 \times 6 = 48$. Remaining $= 144$ man-days. Now $12$ men work: time $= \dfrac{144}{12} = 12$ days.

Asked in: IMO

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