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      Question

      Tap ‘A’ and tap ‘B’ can fill a tank in 42 hours

      and 30 hours, respectively. If both taps are opened together, then find the time after which tap ‘A’ must be closed so the whole tank can be filled in 20 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

      Solution

      Let total capacity of the tank is 210 litres (LCM of 42 and 30) Quantity of water filled by tap ‘A’ in one hour = 210/42 = 5 litres Quantity of water filled by tap ‘B’ in one hour = 210/30 = 7 litres Let tap ‘A’ is closed after ‘x’ hours So, 12 × x + 7 × (20 – x) = 210 Or, 5x = 70 Or, x = 14 hours

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