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      Question

      Tap ‘A’ and tap ‘B’ can fill a tank in 45 hours

      and 40 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 24 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 360 litres (LCM of 45 and 40) Quantity of water filled by tap ‘A’ in one hour = 360/45 = 8 litres Quantity of water filled by tap ‘B’ in one hour = 360/40 = 9 litres Let tap ‘A’ is closed after ‘x’ hours So, 17 × x + 9 × (24 – x) = 360 Or, 8x = 144 Or, x = 18 hours

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