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      Question

      A mixture contains (3x + 60) litres of alcohol and (4x

      – 40) litres of spirit. 20% of the mixture is taken out, and some quantity of alcohol and spirit which is equal to 30% of the quantity of alcohol and spirit respectively in the initial mixture is added to the taken out mixture such that the ratio of alcohol to spirit in the taken out mixture becomes 5:6. The total initial quantity of the mixture can be: I. 7x + 20 litres II. (5x + 580) litres III. (4x + 860) litres
      A Only I Correct Answer Incorrect Answer
      B Only II Correct Answer Incorrect Answer
      C Only I and II Correct Answer Incorrect Answer
      D Only II and III Correct Answer Incorrect Answer
      E All I, II and III Correct Answer Incorrect Answer

      Solution

      According to the question, {0.20(3x + 60) + 0.30(3x + 60)}/{0.20(4x - 40) + 0.30(4x - 40)} = 5/6 (3x + 60)/(4x – 40) = 5/6 Or, 18x + 360 = 20x – 200 Or, x = 560/2 = 280 litres Therefore, total quantity of the mixture = (3x + 60 + 4x – 40) = 1980 litres For I: Total quantity of the mixture = 7x + 20 = 7 × 280 + 20 = 1980 litres Therefore, I can be the answer. For II: Total quantity of the mixture = (5x + 580) = (5 × 280 + 580) = 1980 litres Therefore, II can be the answer. For III: Total quantity of the mixture = (4x + 860) = (4 × 280 + 860) = 1980 litres Therefore, III can be the answer.

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