Multiple choice

$A$ is thrice as good as workman as $B$ and therefore is able to finish a job in $60$ days less than $B$. Working together, they can do it in:

  1. $20$ days
  2. $22\cfrac{1}{2}$ days
  3. $25$ days
  4. $30$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If B takes x days, A takes x/3 days. x - x/3 = 60, so 2x/3 = 60, x = 90. A takes 30 days, B takes 90 days. Together, they take (30 * 90) / (30 + 90) = 2700 / 120 = 22.5 days.

AI explanation

Using the efficiency ratio method, let A's efficiency be 3 units per day and B's be 1 unit per day, making their total work equal to the difference in their individual times multiplied by B's efficiency: 60 * (3 - 1) = 120 units. Working together, their combined efficiency is 4 units per day. Dividing the total work by their combined efficiency yields 120 / 4 = 22.5 days.

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