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 desired price.

Mean Price:

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

Rule of Alligation:

If two ingredients are mixed, then

\([ \frac { \text{Qunatity of cheaper} } { \text{Quantity of dearer} } ]\) = \([\frac { \text{c.p of dearer-Meanprice} } {\text{Mean price - C.P od dearer} } ]\)

We present as under:

 (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).

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 = \([X[1- \frac { Y } { X } ]^n]\)units