Mixing of two or more qualities of things
produces a mixture. When two items of different qualities are thus mixed, the
quality of the resultant mixture lies in between the qualities of the original
constituent items, i.e., it will be higher than the lowest quality and lower
than the highest quality of the items being mixed. .
In the above example that we took, the “quality”
that we looked at was the height of the students. We could also have taken
their weights or the marks scored by them or any other “quality” and calculated
the “weighted average” value of that particular “quality” for the entire group.
.
Similarly, if two types of a product of
different prices per unit are mixed, the unit price of the resultant mixture
will lie between the prices of the two types that form the mixture. .
Here, the average quality is essentially the
weighted average of the two constituent items. .
If q1 is the quantity (or number
of items) of one particular item of quality p1, and q2 be
the quantity (or number of items) of the second item of quality p2
are mixed together to give a new mixture, then the weighted average value (p)
of the quality of the mixture is given by
p = 
Some solved example
example.1
The average weight of a group of 4 girls is
25 kg. A girl joins them and the average weight of the group goes up by 1 kg.
Find the weight of the girl who joined. .
Solution
Total
weight of the 4 girls = (4) (25)
= 100 kg
Total weight of 5 girls after the girl joins
them = (5) (26) = 130 kg
Weight of the girl who joined = 130 – 100
= 30 kg
Example.2
4 kg of rice costing Rs.6 per kg is mixed
with 8 kg of rice costing Rs.12 per kg. Find the cost of the mixture in Rs. per
kg. .
Solution
Cost of
4 kg of rice = (4) (6) = Rs.24 .
Cost of 8 kg of rice = (8) (12) = Rs.96 .
Total cost of 12 kg of rice = 24 + 96 = Rs.120
.
Cost of the mixture = 120/12 = Rs.10 per kg.
.
Example.3
Find the quantity of tea costing Rs.12 per
kg to be mixed with 18 kg of tea costing Rs.9 per kg to form a mixture costing Rs.10.2
per kg. .
Solution
By alligation
rule,
= 
Quantity of tea costing Rs.12 per kg = 
(18) = 12kg
