Mixtures and Alligations Tricks, Formulas, Important shortcuts with examples

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Mixtures and Alligations is a fast and effective technique to back-calculate weights or corresponding averages from a known weighted average. In this article, we will look at all possible Mixtures and Alligations tricks to crack the aptitude problems based on this topic.


Mixtures and Alligations Concept

Alligation is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price. The cost price of a unit quantity of such a mixture is called it's Mean Price.

Remember the rule that cost price of costlier ingredient > cost price of mixture > cost price of cheaper ingredient.

Example: For a simpler way of understanding, consider an example of a typical mixture containing two kinds of substances that do not react with each other. It can be solid in solid, solid in liquid or liquid in liquid. In a mixture of A and B present in a ratio of 3 : 2, we can say that the concentration of A is 3/5 and that of B is 2/5. Let p1, p2 and p be the concentrations of first, second and final mixtures respectively. And q1, q2 and q be their quantities respectively. Then, the final concentration can be determined using the concept of weighted average which gives Mixtures and Alligations formulas:

 mixtures and alligations formulas

The above equation can also be written as

 mixtures and alligations formulas


mixtures and alligations formulas


Type of Mixtures and Alligations Questions

The various types of questions based on Mixtures and Alligations concept are listed below.

  • Type 1: You will receive the quantity of ingredients and their price, you will be asked to find the average price of the resulting mixture.
  • Type 2: You will receive a desired quantity/price of the mixture as well as the price of the ingredients. You need to know in what ratio/percentage of ingredients to mix to get the desired amount.
  • Type 3: Find the resulting amount when concentrating/diluting the mixture.
  • Type 4: Determine the ratio in which 2 quantities should be mixed so that the resulting mixture can be sold. The mixture can be sold for a profit x%.


Mixtures and Alligations Tricks

Here is a modified form of finding the weighted average. Say for examples, 2 ingredients are mixed in a ratio and the cost price of the unit quantity of the mixture (mean price) is given, then

mixtures and alligations questions formulas


Mixtures and Alligations Questions

Example 1:

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

Here is the solution:

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.
C.P. of 1 kg of the mixture = 100/110×68.20= Rs. 62
By the rule of Mixtures and Alligations, we have

mixtures and alligations questions and solutions

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