Multiple choice

A and B together can complete some work in 36 days. B and C together can complete the same work in 60 days. A and C together can complete the same work in 45 days. In how many days can B alone complete the same work?

  1. 180 days

  2. 60 days

  3. 100 days

  4. 90 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given 1/A + 1/B = 1/36, 1/B + 1/C = 1/60, and 1/A + 1/C = 1/45. Adding these gives 2(1/A + 1/B + 1/C) = 1/36 + 1/60 + 1/45 = 12/180 = 1/15. Thus, 1/A + 1/B + 1/C = 1/30. Subtracting (1/A + 1/C) from this gives 1/B = 1/30 - 1/45 = 1/90, so B takes 90 days.

AI explanation

Assume the total job is 360 units. The daily outputs are A + B = 10 units, B + C = 6 units, and A + C = 8 units. Adding these three equations together gives 2(A + B + C) = 24, so A + B + C = 12 units per day. To find B's daily output alone, subtract the combined output of A and C from this total: B = 12 - 8 = 4 units per day. Therefore, B alone requires 360 / 4 = 90 days to finish the job.

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