Multiple choice

A, B and C together can do a piece of work in 3 days. A alone can do it in 9 days and B alone can do it in 6 days. In how many days can C do it alone?

  1. 21

  2. 16

  3. 12

  4. 18

  5. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combined rate of A+B+C is 1/3. A's rate is 1/9, B's rate is 1/6. C's rate = 1/3 - (1/9 + 1/6) = 1/3 - (2/18 + 3/18) = 6/18 - 5/18 = 1/18. Thus C takes 18 days.

AI explanation

Using the LCM method, let the total work be the least common multiple of 3, 9 and 6, which is 18 units. The efficiency of A, B and C together is 18 / 3 = 6 units per day. A's efficiency is 18 / 9 = 2 units per day, and B's efficiency is 18 / 6 = 3 units per day. C's efficiency is 6 - 2 - 3 = 1 unit per day. Therefore, C alone can complete the 18 units of work in 18 / 1 = 18 days.

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