As the dictionary meaning of Alligation (mixing), we will deal with problems related to mixing of different compounds or quantities. The concept of alligation and weighted average are the same.
When two or more quantities are mixed together in different ratios to form a mixture, then ratio of the quantities of the two constituents is given by the following formulae:

Qc/Qd = D-m/ m-C

Qc - Cheaper quantity
Qd - Dearer quantity
c - C.P. of unit qty of 1st constituent.
d - C.P. of unit qty of 2nd constituent.
m - Mean Cost price of unit qty of mixture

Gives us the ratio of quantities in which the two ingredients should be mixed to get the mixture.

Ex.2 A sum of Rs 39 was divided among 45 boys and girls. Each girl gets 50 paise, whereas a boy gets one rupee. Find the number of boys and girls.

Sol. Average amount of money received by each =
Amount received by each girl = 50 paise = Rs 1/2
Amount received by each boy = Re. 1
By alligation rule:
Number of girls
Number of boys =
Number of boys = 33

Number of girls = 45 - 33 = 12.

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