Multiple choice

A and B can finish a work in 18 days, B and C can finish the same work in 24 days, and A and C can finish it in 36 days. A, B and C together can finish the work in

  1. 16 days

  2. 27 days

  3. 30 days

  4. 34 days

  5. 45 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1/A + 1/B = 1/18, 1/B + 1/C = 1/24, 1/A + 1/C = 1/36. Adding these: 2(1/A + 1/B + 1/C) = 1/18 + 1/24 + 1/36 = (4+3+2)/72 = 9/72 = 1/8. So 1/A + 1/B + 1/C = 1/16. Together they take 16 days.

AI explanation

Using the least common multiple method, let the total work be 72 units. The efficiencies of A and B is 4 units per day, B and C is 3 units per day, and A and C is 2 units per day. Adding these three equations gives 2(A + B + C) = 9 units per day, so the combined efficiency of A, B and C is 4.5 units per day. Dividing the total work of 72 units by 4.5 units per day yields 16 days.

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