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      Question

      The ratio of juice to soda in an 84-liter mixture (juice

      + soda) is 9:5. A certain quantity of this mixture is taken out and replaced with the same quantity of soda. If the final mixture has a ratio of 3:4 for juice and soda, respectively, determine the quantity of the mixture that has been taken out.
      A 15 liters Correct Answer Incorrect Answer
      B 25 liters Correct Answer Incorrect Answer
      C 45 liters Correct Answer Incorrect Answer
      D 28 liters Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      ATQ, Initial quantity of Juice in the mixture = 84 ├Ч (9/14) = 54 liters Initial quantity of Soda in the mixture = 84 ├Ч (5/14) = 30 liters Let the quantity of mixture that has been taken out be тАШ14mтАЩ liters So, quantity of Juice that has been taken out = 14m ├Ч (9/14) = тАШ9mтАЩ liters Quantity of Soda that has been taken out = 14m ├Ч (5/14) = тАШ5mтАЩ liters According to question: {(54 тАУ 9m)/(30 тАУ 5m + 14m)} = (3/4) Or, 4 ├Ч (54 тАУ 9m) = 3 ├Ч (30 + 9m) Or, 72 тАУ 12m = 30 + 9m Or, 21m = 42 Or, m = 2 Quantity of mixture that has been taken out = 14 ├Ч 2 = 28 liters.

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