Arithmatical – Alligation or Mixture
DIRECTIONS : Important Facts and Formulae
1.  Alligation : 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. 

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

3.  Suppose a container contains x of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid = [x(1y/x)^{n}] units. 

4.  Rule of Alligation: 

If two ingredients are mixed, then 
Quantity of cheaper  =  C.P. of dearer  Mean Price  
Quantity of dearer  Mean price  C.P. of cheaper 
We present as under : 

C.P. of a unit quantity of cheaper 
C.P. of a unit quanitity of dearer


(Cheaper quantity) : (Dearer quantity) = (dm):(mc). 