Multiple choice

$A$ is three times more efficient worker than $B$ and is therefore able to complete a work in $60$ days less than $B$. What is the number of days that $A$ and $B$ together will take to complete the work?

  1. $22.5$ days
  2. $22$ days
  3. $24.5$ days
  4. $24$ days
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A Correct answer
Explanation

Efficiency ratio A:B = 3:1. Time ratio A:B = 1:3. Let A take x days, B takes 3x days. 3x - x = 60 -> 2x = 60 -> x = 30. A takes 30 days, B takes 90 days. Combined rate = 1/30 + 1/90 = 4/90 = 2/45. Time = 45/2 = 22.5 days.

AI explanation

Using the efficiency method, if A is three times more efficient than B, the ratio of their daily work is 4 to 1, meaning A takes 1/4 of the time B takes. The difference in their times is 60 days, so B alone takes 80 days and A alone takes 20 days. Their combined one day work is 1/20 + 1/80 = 5/80 = 1/16. Working together, they complete the job in 22.5 days.

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