Multiple choice

A and B together can complete a work in 15 days. B and C together can complete the same work in 20 days. A and C together can complete the work in 30 days. What is the respective ratio of the number of days taken by A while completing this work alone to the number of days taken by C while completing this work alone?

  1. 1 : 3

  2. 3 : 1

  3. 1 : 2

  4. 1 : 4

  5. 4 : 1
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A Correct answer
Explanation

Solving the system: 1/A + 1/B = 1/15, 1/B + 1/C = 1/20, 1/A + 1/C = 1/30. Adding first two and subtracting third gives 2/B = 1/12, so B = 24 days. Then 1/A = 1/15 - 1/24 = 1/40, so A = 40 days. And 1/C = 1/20 - 1/24 = 1/120, so C = 120 days. The ratio A:C = 40:120 = 1:3.

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