$30$ men can build a road in $20$ days. After they work for $4$ days, $10$ more men join. The total time…

$30$ men can build a road in $20$ days. After they work for $4$ days, $10$ more men join. The total time taken is:
  1. $14$ days
  2. $15$ days
  3. $16$ days
  4. $18$ days

Solution

Total work $= 30 \times 20 = 600$ man-days. In $4$ days: $30 \times 4 = 120$. Remaining $480$. $40$ men take $\dfrac{480}{40} = 12$ more days. Total $= 4 + 12 = 16$ days.

Asked in: IMO

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