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      Question

      A mixture consists of (k+16)

      liters of milk and (2k+12) liters of water. After adding 8 liters of milk and 20 liters of water to the mixture, the ratio of milk to water becomes 3:5. Determine the initial total volume of the mixture.
      A 112 litres Correct Answer Incorrect Answer
      B 84 litres Correct Answer Incorrect Answer
      C 108 litres Correct Answer Incorrect Answer
      D 100 litres Correct Answer Incorrect Answer
      E 96 litres Correct Answer Incorrect Answer

      Solution

      Let the final quantity of milk be '3y' litres

      Final quantity of water = (5/3) X 3y = '5y' litres

      So, (k + 16 + 8) :(2k + 12 + 20) = 3y:5y

      Or, (k + 24) :(2k + 32) = 3:5

      Or, 5 X (k + 24) = 3 X (2k + 32)

      Or, 5k + 120 = 6k + 96

      Or, 'k' = 24

      Initial quantity of mixture = k + 16 + 2k + 12 = 3k + 28 = 3 X 24 + 28 = 100 litres

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