Multiple choice

A workshop has three workers: A, B, and C. A can complete a task in 20 days, B can complete it in 25 days, and C can complete it in 30 days. If A and B work together for 10 days, and then C alone finishes the task, how many days does C take to complete the remaining work?

  1. 3 days

  2. 4 days

  3. 6 days

  4. 7 days

  5. None of these
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A Correct answer
Explanation

A's rate is 1/20 and B's rate is 1/25. In 10 days, they complete 10 * (1/20 + 1/25) = 10 * (5/100 + 4/100) = 10 * (9/100) = 0.9 of the task. The remaining 0.1 of the task is completed by C, whose rate is 1/30; thus, C takes 0.1 / (1/30) = 3 days.

AI explanation

Using the least common multiple method, let the total work be the LCM of 20, 25, and 30, which is 300 units. The daily work rates for A, B, and C are 15, 12, and 10 units per day respectively. A and B have a combined rate of 27 units per day, so working for 10 days they complete 270 units of the task. This leaves 30 units of work remaining for C, who works at 10 units per day, meaning C will take 3 days to finish the remaining work.

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