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      Question

      The question consists of two statements numbered “I

      and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A container has a mixture of Soda and Water in the ratio 9:5. Find the total volume of the mixture. Statement I: If 140 ml of the mixture is removed and then 60 ml of water is added to what remains, the proportion of Soda in the final mixture becomes 50%. Statement II: If 210 ml of the mixture is removed and then ‘y’ ml of water together with (y + 50) ml of Soda is added, the quantity of Soda in the new mixture will be 90 ml more than the quantity of water.
      A The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. Correct Answer Incorrect Answer
      C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
      D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
      E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ, Let original quantity of Soda and water in the mixture is 9x ml and 5x ml respectively. Statement I: Quantity of Soda in 140 ml of mixture = 9/14 × 140 = 90 ml Quantity of water in 140 ml of mixture = 5/14 × 140 = 50 ml According to question; 9x – 90 = 5x – 50 + 60 Or, 4x = 100 Or, x = 25 Total quantity of original mixture = 14 × 25 = 350 ml So, data in statement I alone is sufficient to answer the question. Statement II: Quantity of Soda in 210 ml of mixture = 9/14 × 210 = 135 ml Quantity of water in 210 ml of mixture = 5/14 × 210 = 75 ml According to question; 9x – 135 + y + 50 = 5x – 75 + y + 90 Or, 4x = 100 Or, x = 25 Total quantity of original mixture = 14 × 25 = 350 ml So data in statement II alone is sufficient to answer the question

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