Multiple choice

A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days, altogether, was the work completed?

  1. 6

  2. 8

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A and C's combined rate is 1/10 + 1/20 = 3/20. In 2 days, they finish 2 * (3/20) = 6/20 = 3/10 of the work. Remaining work is 7/10. B and C's combined rate is 1/15 + 1/20 = 7/60. Time taken to finish the remaining work is (7/10) / (7/60) = 6 days. Total time = 2 + 6 = 8 days.

AI explanation

Assume the total work is the least common multiple of 10, 15 and 20, which is 60 units. The daily work units of A, B and C are 6, 4 and 3 respectively. A and C work for 2 days to complete 2 times 9 units, leaving 42 units. B and C work together at 7 units per day, taking 6 more days. The total time is 2 days plus 6 days, which equals 8 days.

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