Multiple choice

A team consists of three workers: X, Y, and Z. X and Y together can complete a certain task in 15 days, while Y and Z together can complete the same task in 20 days. If X is three times as efficient as Z, how many days does it take for Y to complete the task alone?

  1. 24

  2. 30

  3. 36

  4. 40
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A Correct answer
Explanation

Let X, Y, Z be their daily work rates. X+Y = 1/15, Y+Z = 1/20. Given X = 3Z. Substituting X: 3Z+Y = 1/15 and Y+Z = 1/20. Subtracting the equations: 2Z = 1/15 - 1/20 = 1/60, so Z = 1/120. Then Y = 1/20 - 1/120 = 5/120 = 1/24. Y takes 24 days.

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