Multiple choice

Together X and Y can complete a piece of work in 9 days, Y and Z in 12 days and X and Z in 18 days. Who is the most efficient worker among X, Y and Z?

  1. X

  2. Y

  3. Z

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let X, Y, Z be their rates. X+Y = 1/9, Y+Z = 1/12, X+Z = 1/18. Adding these: 2(X+Y+Z) = 1/9 + 1/12 + 1/18 = (4+3+2)/36 = 9/36 = 1/4. So X+Y+Z = 1/8. Then Z = 1/8 - 1/9 = 1/72; X = 1/8 - 1/12 = 1/24; Y = 1/8 - 1/18 = 5/72. Comparing 1/24, 5/72, 1/72, Y is the largest.

AI explanation

Let the total work be the least common multiple of the days given, which is 36 units. The efficiencies for X and Y, Y and Z, and X and Z are 4, 3, and 2 units respectively. Solving the equations gives individual efficiencies of 1.5 for X, 2.5 for Y, and 0.5 for Z. Because 2.5 is the highest value, Y is the most efficient worker.

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