Multiple choice

Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed?

  1. 9

  2. 8

  3. 6

  4. 10
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A Correct answer
Explanation

Sam's rate = 1/15, Bob's = 1/10, Kim's = 1/30. In 3 days, Sam works 3 days, Bob 1, Kim 1. Work = 3(1/15) + 1/10 + 1/30 = 1/5 + 3/30 + 1/30 = 6/30 + 3/30 + 1/30 = 10/30 = 1/3. In 9 days, they complete 3 * (1/3) = 1 job.

AI explanation

Assume the total job is the least common multiple of 15, 10 and 30, which is 30 units. Sam does 2 units per day, so on days 1 and 2 he does 4 units. On the third day, all three work together at 6 units per day, completing 6 units, making the 3-day cycle work 10 units. After two such cycles of 3 days, 20 units are done. The remaining 10 units are finished by all three on day 9, completing the job in 9 days.

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