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      Question

      Tap β€˜A’ and tap β€˜B’ can fill a tank in 45 hours

      and 35 hours, respectively. If both taps are opened together, then find the time after which tap β€˜A’ must be closed so the whole tank can be filled in 21 hours.
      A 16 hours Correct Answer Incorrect Answer
      B 18 hours Correct Answer Incorrect Answer
      C 14 hours Correct Answer Incorrect Answer
      D 32 hours Correct Answer Incorrect Answer
      E 12 hours Correct Answer Incorrect Answer

      Solution

      Let total capacity of the tank is 315 litres (LCM of 45 and 35) Quantity of water filled by tap β€˜A’ in one hour = 315/45 = 7 litres Quantity of water filled by tap β€˜B’ in one hour = 315/35 = 9 litres Let tap β€˜A’ is closed after β€˜x’ hours So, 16 Γ— x + 9 Γ— (21 – x) = 315 Or, 7x = 126 Or, x = 18Β hours

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