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      Question

      A and B together can complete a work in 12 days, B and C

      in 15 days and C and A in 20 days. In how many days can A, B and C individually complete the work?
      A 10, 10 and 60 days Correct Answer Incorrect Answer
      B 20, 40 and 20 days Correct Answer Incorrect Answer
      C 30, 20 and 60 days Correct Answer Incorrect Answer
      D 30, 30 and 30 days Correct Answer Incorrect Answer

      Solution

      Let daily work of A, B, C be a, b, c. a + b = 1/12 b + c = 1/15 c + a = 1/20 Add all: 2(a + b + c) = 1/12 + 1/15 + 1/20 LCM(12, 15, 20) = 60 1/12 = 5/60, 1/15 = 4/60, 1/20 = 3/60 Sum = (5 + 4 + 3)/60 = 12/60 = 1/5 ⇒ a + b + c = 1/10 Now, a = (a + b + c) − (b + c) = 1/10 − 1/15 = (3 − 2)/30 = 1/30 b = (a + b + c) − (c + a) = 1/10 − 1/20 = (2 − 1)/20 = 1/20 c = (a + b + c) − (a + b) = 1/10 − 1/12 = (6 − 5)/60 = 1/60 So, A alone: 30 days B alone: 20 days C alone: 60 days

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