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Alligation Or Mixture


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

A process or rule for the solution of problems concerning the compounding or mixing of ingredients differing in price or quality.

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


Basic formula for mixture and alligation problem:

If two different commodities, one of which is cheaper than the other, are mixed to obtain a new mixture, Cost Price of unit value of this new mixture is called mean price.This is the the first and foremost formula you should remember to solve mixture and alligation questions.

Example: A merchant blends two types of rice costing Rs.15 per kg and Rs.20 per kg .In what ratio should these two rice to be mixed so that resulting mixture may cost Rs.16.50 per kg.


When water is mixed in milk or any liquid in such away that resulting mixture gives a profit of x% when sold at C.P of milk/liquid. Then ratio of Quantity water:Quantity of milk=x:100

Eg: In what ratio should water be mixed in milk so that seller makes a profit of 10% when mixture is sold at cost price of milk? Water : milk =10:100=1:10.


Removal and replacement problems:

A vessel contains x litre of milk. y litre is drawn and replaced by water.Then again y litre of solution is replaced by water. If this process is repeated ‘n’ times,then


Example: 9 litre are drawn from a cask full of milk and then filled with water.9 litre of mixture are drawn and cask is again filled with water.Quantity of milk now left in the cask is to that of water in at is as 16:9.What is the capacity of cask in litre?
Ans:let x be the capacity of cask which is=quantity of initial milk,

For solved problems on above formulas please visit below sections: