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      Question

      A and B can complete a piece of work in 15 days, B and C

      in 30 days and C and A in 45 days. In how many days will they complete the work if they start working together?
      A 8(3/11) Correct Answer Incorrect Answer
      B 11(1/3) Correct Answer Incorrect Answer
      C 11(2/3) Correct Answer Incorrect Answer
      D 16(4/11) Correct Answer Incorrect Answer

      Solution

      Let the work rates of A, B, and C be A, B, and C respectively. A + B = 1/15 B + C = 1/30 C + A = 1/45 Adding these three equations: (A + B) + (B + C) + (C + A) = 1/15 + 1/30 + 1/45 ⇒ 2A + 2B + 2C = 1/15 + 1/30 + 1/45 ⇒ 2(A + B + C) = (6 + 3 + 2) / 90 ⇒ 2(A + B + C) = 11 / 90 ⇒ A + B + C = 11 / 180 Time taken when A, B, and C work together = 1 / (A + B + C) ⇒ Time = 1 / (11 / 180) ⇒ Time = 180 / 11 ⇒ Time = 16 (4/11) days

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