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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 which of the following relation is correct. Quantity I: Value of ‘X’ Quantity II: Value of ‘Y + 40’
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      D Quantity I ≤ Quantity II Correct Answer Incorrect Answer
      E Quantity I = Quantity II or No relation Correct Answer Incorrect Answer

      Solution

      Mixture contains total (X + Y) liters ATQ, = X² + XY – 30X = XY + Y² – 30Y + 30X + 30Y ⇒ X² – Y² = 60X …(i) And, 2X² + 2XY – 120X = XY + Y² – 60Y + 60X + 60Y 2X 2 + XY = 180X +Y 2 …(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 Quantity I: X = 80lt Quantity II: Y + 40 = 40 + 40 = 80ℓ Quantity I = Quantity II

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