Alligations

To discuss alligations rule, read the question below:

Solution:

The following figure illustrates the alligations rule:

The alligations rule can also be written more easily as follows:

Apply the data values in the alligations rule as below:

Cost of Dearer (costlier), d = 40,

Cost of cheaper, c = 32,

Cost of mixture (mean price), m = 35

Therefore, from alligations rule:

The ratio in which dearer is to be mixed with the cheaper is

d – m: m – c = 40 – 35: 35 – 32 =

5: 3

Example 2:

An amount of Rs. 10000 was divided among 40 students consisting of boys and girls. Each boy received Rs. 300 while each girl received Rs. 150. Find the number of boys and girls.

Solution:

Apply the question data in the variables in the alligations rule

Mean value of the share of all the 40 students is 10000/40 = 250

Let share of each boy = d = 300,

Share of each girl = c = 150,

Share of each student = m = 250

Therefore, from alligations rule we have

ratio of girls: boys = d – m: m – c

300 – 250: 250 – 150 = 50: 100 = 1: 2