Multiple choice

If A and B can do a piece of work in 6 days, B and C in 8 days and C and A in 12 days, then A alone can do the work in how many days?

  1. 16 days

  2. 24 days

  3. 18 days

  4. 152/3 days

  5. Cannot be determined
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A Correct answer
Explanation

Let rates be A+B=1/6, B+C=1/8, C+A=1/12. Adding these: 2(A+B+C) = 1/6 + 1/8 + 1/12 = (4+3+2)/24 = 9/24 = 3/8. So A+B+C = 3/16. A = (A+B+C) - (B+C) = 3/16 - 1/8 = 3/16 - 2/16 = 1/16. Thus, A takes 16 days.

AI explanation

Using the LCM method, let the total work be the least common multiple of 6, 8, and 12, which is 48 units. The combined rates of (A+B), (B+C), and (C+A) are 8, 6, and 4 units per day respectively. Adding these gives 2(A+B+C) = 18 units per day, so the combined rate of A+B+C is 9 units per day. A's rate is the total rate minus B+C's rate: 9 - 6 = 3 units per day. Therefore, A alone can complete the 48 units of work in 48 / 3 = 16 days.

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