Question
A and B together can complete a work in 15 days, while B
and C together can complete the same work in 20 days. If A, B, and C together can complete the work in 12 days, how many days will B take to complete the work alone?Solution
Let the work done by A in 1 day be A, by B in 1 day be B, and by C in 1 day be C. A + B can complete the work in 15 days → A + B = 1/15 B + C can complete the work in 20 days → B + C = 1/20 A + B + C can complete the work in 12 days → A + B + C = 1/12 Next, subtract (B + C) from (A + B + C): (A + B + C) - (B + C) = 1/12 - 1/20 A = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 So, A’s rate of work = 1/30. Now, from (A + B) = 1/15, we know that A + B = 1/15. Substitute A = 1/30: 1/30 + B = 1/15 B = 1/15 - 1/30 = 2/30 - 1/30 = 1/30 Therefore, B alone can complete the work in 30 days. Correct option: c
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