$15$ men working $9$ hours a day can build a wall in $6$ days. How many days will $18$ men working $8$ hours…

$15$ men working $9$ hours a day can build a wall in $6$ days. How many days will $18$ men working $8$ hours a day take to build the same wall?
  1. $\dfrac{15}{4}$ days
  2. $\dfrac{45}{8}$ days
  3. $5$ days
  4. $6$ days

Solution

Total man-hours $= 15 \times 9 \times 6 = 810$. Required: $18 \times 8 \times d = 810 \Rightarrow d = \dfrac{810}{144} = \dfrac{45}{8}$ days.

Asked in: IMO

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