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      Question

      A pipe can fill a tank in 14 hours, and B pipe

      can drain a tank in 21 hours. If a system of N pipes (fill pipes and drain pipes put together) can fill the tank in exactly 7 hours, which of the following are possible values of N (More than one option could be correct)? (1) 21 (2) 13 (3) 18 (4) 24 (5) None of these
      A 1 and 2 only Correct Answer Incorrect Answer
      B 1 and 3 only Correct Answer Incorrect Answer
      C 2 and 4 only Correct Answer Incorrect Answer
      D 2 and 3 only Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let no. of filling pipes = x So number of drain pipes = N - x; A : B = 14 : 21 Total capacity of Tank = LCM of 14 & 21 = 42L 1 hr work = 2 : -3 So According to the question, 2x - 3(N-x) = 42/7 5x - 3N = 6 5x = 6 + 3N So by putting option (1), 5x = 6 + 3 × 21 = 6 + 63 = 69 so x = 13.8 which is not possible as number of pipes cannot be in decimals; By putting (2) option, 5x = 6 + 3 × 13 = 6 + 39 = 45 x = 45/5 = 9 which is possible; By putting (3) option, 5x = 6 + 3 × 18 = 6 + 54 = 60 so x = 12 which is also possible; By putting (4) option. 5x = 6 + 3 × 24 = 6 + 72 = 78 x = 78/5 = 15.6 which is not possible, Hence (2) & (3) are possible.

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