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 p1, p2 and p be the concentrations of the first, second and final mixtures respectively. Let q1, q2 and q be their quantities respectively.
Then the final concentration can be determined using the rule for weighted averages which gives:
p = (p1q1 + p2q2) / (q1 + q2)
This formula can be extended even if more than 2 mixtures are present.
The equation above can be rewritten as q1/q2 = (p2 - p) / (p - p1)
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: