Multiple choice

A, B and C together can finish a work in 4 days. If A alone can finish the same work in 12 days and B in 18 days, in how many days can C alone finish the same work?

  1. 9 days

  2. 6 days

  3. 12 days

  4. 18 days

  5. 24 days
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A Correct answer
Explanation

The combined rate of A, B, and C is 1/4. A's rate is 1/12 and B's rate is 1/18. C's rate = 1/4 - (1/12 + 1/18) = 1/4 - (3/36 + 2/36) = 1/4 - 5/36 = 9/36 - 5/36 = 4/36 = 1/9. Thus, C takes 9 days.

AI explanation

Using the LCM method, let the total work be the LCM of 4, 12, and 18, which is 36 units. The combined efficiency of A, B, and C is 36 divided by 4, or 9 units per day. A's efficiency is 36 divided by 12, or 3 units per day, and B's efficiency is 36 divided by 18, or 2 units per day. C's efficiency is 9 minus 3 minus 2, giving 4 units per day. The time taken by C alone is 36 divided by 4, resulting in 9 days.

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