 # 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: The above equation can also be written as or ## 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

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 ### >> Practice more problems on Mixtures & Alligations

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