**Alligation**

Allegation 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.**Mean Price**

The cost price o a unit quantity of the mixture is called the mean price.**Rule of Alligation**

If two ingredients are mixed, then

Quantity of cheaper

Quantity of dearer= (C.P of dearer) - (Mean Price)

(Mean Price) - (C.P of cheaper)

We present as under:

(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}