Mixture and Alligation Concepts

Understanding the Concepts of Mixture and Alligation

Following is an overview of the Mixture and Alligation, as well as many examples, to help learners in understanding the concepts.

Listed below are the different concepts:

1. Mixture
2. Alligation
3. Mean Price

1. Mixture

It is formed by combining two or more different kinds of quantities.

Types of Mixture

1.1. Simple Mixture

A simple mixture is generated when two or more separate elements are combined together.

Example: Apple shake

A simple Mixture can be properly represented using the diagram below.

1.2. Compound Mixture

A compound mixture is produced when two or more simple mixture are combined.

Example: Coffee soda

2. Alligation

Alligation is a way of resolving mathematical problems involving element combinations. This rule allows us to determine the ratio in which two or more ingredients at the particular price must be blended to attain the desired price mixture.

3. Mean Price

The cost price of a unit quantity of a mixture made by combining two or more elements.

These concepts can be solved by the following methods

1. Formula Method
2. Criss-Cross Method

3.1. Formula Method

The general formula to find the ratio of ingredients in the mixture is:

(Quantity of cheaper/ Quantity of dearer) = ((Cost price of Dearer- Mean price) / (Mean price – cost price of the cheaper))

Let's understand the formula method better with an example:

Example Problem

In what proportion must tea at Rs. 7.50 per kg be mixed with tea at Rs. 10.50 per kg to produce a mixture worth Rs. 8.50 per kg?

Solution

Applying the formula method with the given data,we get ,

(Quantity of cheaper(X)/ Quantity of dearer(Y)) = ((Cost price of Dearer(10.5Rs)- Mean price(8.5Rs)) / (Mean price(8.5Rs) – cost price of the cheaper(7.5Rs))

⇒ X/Y = (10.5 - 8.5)/(8.5 - 7.5)

⇒ X/Y = 2/1

So we get the final ratio as 2 : 1.

3.2. Criss-Cross Method

The criss-cross method can be expressed using a diagram:

Let's understand the criss-cross method better with an example:

Example Problem

In what proportion must tea at Rs. 7.50 per kg be mixed with tea at Rs. 10.50 per kg to produce a mixture worth Rs. 8.50 per kg?

Solution

Using the criss-cross method,we get the answer as 2 : 1.