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.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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