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      Question

      A container has 'x' litres of a 30% sugar solution.

      Another container has 40 litres of a 50% sugar solution. When both solutions are mixed together, the resulting mixture is 40% sugar. Then 20 litres of this mixture is removed and replaced by pure water. What is the final concentration of sugar in the resulting solution?
      A 15% Correct Answer Incorrect Answer
      B 27% Correct Answer Incorrect Answer
      C 30% Correct Answer Incorrect Answer
      D 37% Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, After mixing: Total volume = x + 40 litres Sugar from first container = 0.30x litres Sugar from second container = 0.50 × 40 = 20 litres Given the resulting mixture is 40% sugar: (0.30x + 20) / (x + 40) = 0.40 0.30x + 20 = 0.40x + 16 20 − 16 = 0.40x − 0.30x 4 = 0.10x x = 40 litres So total volume after mixing = 40 + 40 = 80 litres Sugar = 40% of 80 = 0.40 × 80 = 32 litres Now 20 litres of mixture is removed and replaced by water. Sugar removed = 32 × (20 / 80) = 8 litres Sugar left = 32 − 8 = 24 litres Total volume after removal = 80 − 20 = 60 litres Then 20 litres of pure water added → final volume = 80 litres Final concentration of sugar = (24 / 80) × 100% = 30%

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