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Mixture and Alligation

Mixture and Alligation

Mixture and alligation is an integral topic in the Quantitative section of the CAT exam. There are a lot of questions asked every year from this topic and thus, is very crucial from the examination point of view. So, here is an explanation of the Mixture and Alligation along with various illustrations to help the candidates learn the topic with ease.

Definitions of Mixture and Alligation

Here are some important definitions related to mixtures and alligation that would help to tackle the related questions with ease.

Mixtures

When two or more components are mixed in a certain ratio, a mixture is created.

Types of mixtures

  • Simple Mixtures: When two or more different ingredients are mixed together, a simple mixture is formed.
  • Compound Mixtures: When two or more simple mixtures are mixed together, a compound mixture is formed.

Alligation

To understand the concept of alligations, let’s take an example and look at it from all angles possible.
Example 1:
30 boys with an average weight of 60 kgs and 20 girls with an average weight of 40.Find the average weight of the whole class? Find the average weight of the whole class?
Solution:
To find the answer to the above question, one can use the formula for weighted average. Suppose the question was framed a bit differently, the Average weight of boys is 60, the average weight of girls is 40 and average weight of the whole class is 52.
Find the ratio between the number of boys and girls
Solution:
The fastest way to solve this question would be by using Alligation. Read below for its solution using alligation.
So what exactly is Alligation?
It is the reverse of weighted average; i.e. If the averages of two groups are separately given and the average of the whole group is given, then we can find out the ratio between the groups.
For example, in the above question, the data given is-
Average weight of boys=60, average weight of girls=40 and average weight of the whole class is =52
The data can be represented in an Alligation chart as given below and use it to find the ratio between the number of boys and girls in the class.

Take the difference across: x= 60-52=8 and y= 52-40=12. That is how we get the ratio between the boys and girls as 12:8 or 3:2.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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