Multiple choice

A, B and C complete a work working alone in 10, 15 and 20 days respectively If all of then work together to complete the work what fraction of the work would have done by B?

  1. $\displaystyle \frac{4}{13}$
  2. $\displaystyle \frac{1}{2}$
  3. $\displaystyle \frac{1}{3}$
  4. $\displaystyle \frac{6}{13}$
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A Correct answer
Explanation

A, B, and C complete work in 10, 15, and 20 days. Their rates are 1/10, 1/15, and 1/20. Total rate = 6/60 + 4/60 + 3/60 = 13/60. The fraction of work done by B is (Rate of B) / (Total Rate) = (1/15) / (13/60) = 4/13.

AI explanation

Assume the total work is the least common multiple of 10, 15, and 20, which is 60 units. The daily work capacities of A, B, and C are 6 units, 4 units, and 3 units respectively, giving a combined daily capacity of 13 units. The fraction of the work done by B is the ratio of B's daily work to the total daily work, which is 4 divided by 13.

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