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A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Question and options

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. 12 days
  2. 15 days
  3. 16 days
  4. 18 days

Answer and explanation

Correct answer: B - 15 days
Rates: A = 120\frac{1}{20}, B = 130\frac{1}{30}, C = 160\frac{1}{60}. In each 3-day cycle work = 320+130+160=960+260+160=1260=15\frac{3}{20} + \frac{1}{30} + \frac{1}{60} = \frac{9}{60} + \frac{2}{60} + \frac{1}{60} = \frac{12}{60} = \frac{1}{5}. So 5 cycles = 15 days.

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