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      Question

      A mixture contains ‘X’ liter milk and ‘Y’ liter

      water. If 30 liter of mixture is taken out and replaced with water, then the quantity of milk and water becomes equal. But, if 60 liter of mixture is taken out and replaced with water, then quantity of milk becomes half of the quantity of water. Find the value of X and Y.
      A 70, 30 Correct Answer Incorrect Answer
      B 80, 50 Correct Answer Incorrect Answer
      C 40, 80 Correct Answer Incorrect Answer
      D 75, 35 Correct Answer Incorrect Answer
      E 80, 40 Correct Answer Incorrect Answer

      Solution

      Mixture contains total (X + Y) liters ATQ,  X– [30X/((X+Y))] = Y– [30Y/(X+Y)]+30    X² + XY – 30X = XY + Y² – 30Y + 30X + 30Y  ⇒ X² – Y² = 60X…(i)  And,  2[X–60X/(X+Y)]=[Y–60Y/(X+Y)+60]  2X² + 2XY – 120X = XY + Y² – 60Y + 60X + 60Y   2X2+ XY = 180X +Y2    …(ii) Subtract (i) from (ii)  X² + XY = 120X  X + Y = 120ℓ      …(iii) But X² – Y² = 60X ⇒ (X + Y) (X – Y) = 60X ⇒ 2 (X – Y) = X ⇒ 2X – 2Y = X ⇒ X = 2Y     …(iv) By using (iii) & (iv) ⇒ Y = 40ℓ  And X = 80ℓ

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