Multiple choice

A and B can do a bit of work in 12 days. B and C can do it in 15 days while C and A can do it in 20 days. In how long will they complete it cooperating? Additionally, in how long can A alone do it?

  1. 10 days, 30 days.

  2. 15 days, 20 days.

  3. 20 days, 40 days.

  4. 10 days, 50 days.

  5. None of These
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A Correct answer
Explanation

Let rates be A+B=1/12, B+C=1/15, C+A=1/20. Summing these gives 2(A+B+C) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5, so A+B+C = 1/10 (10 days). To find A, subtract B+C: A = 1/10 - 1/15 = 1/30 (30 days).

AI explanation

Add the work rates of the three pairs to get 1/12 + 1/15 + 1/20 = 12/60 = 1/5. This equals twice the combined rate of A, B, and C, so dividing by two gives their combined daily rate of 1/10, meaning they complete the work together in 10 days. The sum of the pairs' rates minus the combined rate yields B and C's rate of 1/10 + 1/15 - 1/10 = 1/15. Subtracting this from the total rate gives A's rate as 1/10 - 1/15 = 1/30, which means A alone takes 30 days.

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