Multiple choice

A is two times as efficient as B and three times as efficient as C. If it takes 20 days for B and C to finish a piece of work together, how many days will all of them take to finish the same piece of work together?

  1. 9 1 11 days

  2. 9 8 9 days

  3. 10 2 11 days

  4. 12 days

  5. None of these
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A Correct answer
Explanation

Let the efficiency of A be 6 units/day, which means B's efficiency is 3 units/day and C's efficiency is 2 units/day. Since B and C together (5 units/day) take 20 days to complete the work, the total work is 5 * 20 = 100 units. Working together, all three have a combined efficiency of 6 + 3 + 2 = 11 units/day, so they will complete the work in 100/11 = 9 1/11 days.

AI explanation

Let A's efficiency be 6 units per day, so B's efficiency is 3 units and C's is 2 units. The total work is completed by B and C in 20 days, meaning the total work is (3 + 2) * 20 = 100 units. When A, B, and C work together, their combined efficiency is 6 + 3 + 2 = 11 units per day. Using the time and work formula, they will finish the 100 units of work in 100/11 days, which equals 9 1/11 days.

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