in a glass of milk, the portion of pure milk and water is 3:1, how much of the mixture must be withdrawn and substituted by water so that the resulting mixture become half pure milk and half pure water

• 1/3 of mixture.
  
  Let there be y L of milk
  ===> 3/4*y is pure milk
  1/4*y is water
  
  Let x be the portion of mixture withdrawn
  Now we have (y-x)L of mixture
  pure milk = 3/4*(y-x)
  water = 1/4*(y-x)
  
  The portion withdrawn is replaced by water (ie x Liters of water is added)
  Quantity of water = 1/4*(y-x)+ x
  
  Since the resulting solution is half pure water, quantity of water is y/2
  ie,
  1/4*(y-x)+ x = y/2
  3/4*x = 1/4*y
  3x = y
  x = 1/3*y
  ===> 1/3 rd of the mixture must be withdrawn and replaced by water.
  
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