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

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