Multiple choice

A and B together can complete a piece of work in 12 days, and B and C together in 15 days. If A is twice as good a workman as C, then in how many days will B alone complete the same work?

  1. 30

  2. 25

  3. 24

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let rates be A, B, C. A+B = 1/12, B+C = 1/15. A = 2C. Substitute: 2C+B = 1/12, B+C = 1/15. Subtracting: C = 1/12 - 1/15 = 1/60. Then B = 1/15 - 1/60 = 3/60 = 1/20. B takes 20 days.

AI explanation

Let the daily work rates of A, B, and C be a, b, and c. Given A is twice as good as C, a equals 2c, so the equation for A and C becomes 2c plus 2c equals 1/10, yielding c equals 1/20 and a equals 1/10. The combined rate of B and C is 1/15, so subtracting C's rate of 1/20 gives B's individual rate as 1/60 plus 1/20, which simplifies to 1/20. Therefore, B alone will complete the work in 20 days.

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