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      Question

      A vessel contains a mixture of milk and water in the

      ratio 3:1. When 12 litres of this mixture are taken out and replaced with pure water, the ratio of milk to water becomes 9:7. What is the initial quantity of the mixture in the vessel?
      A 30 litres Correct Answer Incorrect Answer
      B 50 litres Correct Answer Incorrect Answer
      C 48 litres Correct Answer Incorrect Answer
      D 25 litres Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let initial quantity = V litres. Milk = 3V/4, Water = V/4. When 12 L mixture is removed, milk and water removed are: Milk removed = (3/4)×12 = 9 L Water removed = (1/4)×12 = 3 L Remaining: Milk = 3V/4 − 9 Water = V/4 − 3 Then 12 L pure water is added: New water = V/4 − 3 + 12 = V/4 + 9 New ratio milk : water = 9 : 7: (3V/4 − 9) / (V/4 + 9) = 9 / 7 Cross-multiply: 7(3V/4 − 9) = 9(V/4 + 9) 21V/4 − 63 = 9V/4 + 81 21V/4 − 9V/4 = 81 + 63 12V/4 = 144 3V = 144 V = 48 litres.

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