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Mixtures and Allegations

 Mixtures are formed when two or more quantities of different values are mixed together.

Allegation is a practical method of solving arithmetic problems related to mixtures of ingredients. There are two kinds of problems:

  1. To find the quantity of a mixture given the quantities of its ingredients. (Allegation Medial)
  2. To find the amount of each ingredient needed to make a mixture of a given quantity. (Allegation Alternate)

Important Facts and Formula

Allegation: It is the rule that enables us to find the ratio in which two of more ingredients at the given price must be mixed to produce a mixture of a desired price.

Mean Price: The cost price of a unit quantity of the mixture is called the mean price.

Rule of Allegation: If two ingredients are mixed then Quantity of Cheaper / Quantity of Dearer = (C.P. of Dearer – Mean Price) / (Mean Price – C.P. of Cheaper)






Cheaper quantity : Dearer quantity = (d – m) : (m – c)

Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After n operations the quantity of pure liquid = x (1 – y/x)n units.