$8$ men or $12$ women can complete a piece of work in $25$ days. How many days will $6$ men and $11$ women…

$8$ men or $12$ women can complete a piece of work in $25$ days. How many days will $6$ men and $11$ women take to complete the same work?
  1. $10$ days
  2. $12$ days
  3. $14$ days
  4. $15$ days

Solution

$8$ men $= 12$ women, so $1$ man $= \dfrac{3}{2}$ women. Total work $= 12 \times 25 = 300$ woman-days. $6$ men $+ 11$ women $= 6 \times \dfrac{3}{2} + 11 = 9 + 11 = 20$ women. Days $= \dfrac{300}{20} = 15$.

Asked in: IMO

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