**Mixtures**

Mixtures typically contain two kinds of substances that do not react with each other. Mixtures can be solid in solid, solid in liquid (solution) or liquid in liquid. In a mixture of A and B present in the ratio 3 : 2, we can say that the concentration of A is 3/5 and that of B is 2/5. For solutions, the concentration may be expressed in terms of weight per volume (gm/ml).**Mixing two mixtures**Let p

_{1}, p

_{2}and p be the concentrations of the first, second and final mixtures respectively. Let q

_{1}, q

_{2}and q be their quantities respectively.

Then the final concentration can be determined using the rule for weighted averages which gives:

p = (p

_{1}q

_{1}+ p

_{2}q

_{2}) / (q

_{1}+ q

_{2})

This formula can be extended even if more than 2 mixtures are present.

**Alligation**The equation above can be rewritten as q

_{1}/q

_{2}= (p

_{2}- p) / (p - p

_{1})

A simpler way to understand this would be to consider the mixing of a cheaper and dearer (costlier) item in order to obtain an item of intermediate price. In that case, the equation of alligation can be descriptively written as:

Quantity of cheaper / quantity of dearer = (rate of dearer - average rate) / (average rate - rate of cheaper)

This can be represented pictorially as follows: