Question
A mixture contains βXβ liter milk and βYβ 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 βXβ Quantity II: Value of βY + 40βSolution
Mixture contains total (X + Y) liters ATQ, = XΒ² + XY β 30X = XY + YΒ² β 30Y + 30X + 30Y β XΒ² β YΒ² = 60X β¦(i) And, 2XΒ² + 2XY β 120X = XY + YΒ² β 60Y + 60X + 60Y 2X 2 + XY = 180X +Y 2 β¦(ii) Subtract (i) from (ii) XΒ² + XY = 120X X + Y = 120β β¦(iii) But XΒ² β YΒ² = 60X β (X + Y) (X β Y) = 60X β 2 (X β Y) = X β 2X β 2Y = X β X = 2Y β¦(iv) By using (iii) & (iv) β Y = 40β And X = 80β Quantity I: X = 80lt Quantity II: Y + 40 = 40 + 40 = 80β Quantity I = Quantity II
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