Mixture and Alligation

Alligation is a critical component of quantitative aptitude for various competitive exams. The rule of alligation allows us to determine the ratio in which two or more elements at a particular price must be combined to achieve the desired price mixture. A mixture is created by combining two or more types of proportions. This rule allows us to calculate the ratio in which two or more elements at the same price must be blended to obtain the desired price mixture. On the other hand, a mixture is created by combining two or more quantities. It can be stated as a percentage or as a ratio. This method can be used to solve problems involving mixtures, profit and loss, simple interest, time and distance, percentage, and so on.

Mixture

A mixture consists of two or more components combined in a specific ratio or proportion. Mixtures are materials composed of two or more different types of components. They can be separated through physical means. Examples include a salt and water solution, a sugar and water mixture, different gases, air, etc. Chemical changes do not bring the distinct components of a combination together. As a result, the individual qualities of the components are preserved.

Types of Mixtures

Based on their composition, they can be divided into two types:

1. Homogeneous Mixture

Homogeneous mixtures have a constant composition throughout. Examples include a salt-water solution, a sugar-water solution, lemonade, soda water, etc. A salt solution is a well-known example. This is because the distinction between salt and water is impossible to make here. When a ray of light passes through a mixture of salt and water, the path of light is obscured.

Properties

• All solutions are included in a homogeneous mixture.
• The particles, in this case, are smaller than one nanometer in size.
• No indication of the Tyndall effect has been found.
• It is impossible to identify where a particle’s boundaries are.
• You can’t separate the constituent particles here by centrifugation or decantation.
• Alloys are an example of a solution.

2. Heterogeneous Mixture

Heterogeneous mixes are those in which the composition is not uniform throughout. A mixture of dirt and sand, sulphur and iron filings, oil and water, etc., are heterogeneous because their composition varies. In a homogeneous mixture, the various borders of the constituent particles can be identified. This is because it has two or more distinct phases.

Properties

• Most mixes are heterogeneous, except for solutions and alloys.
• The constituent particles are scattered uniformly.
• The parts are easily distinguishable.
• There are frequently two or more phases in a heterogeneous combination.
• The particles in this image range from one nanometer to one micrometre.

Alligation

It is a method for resolving arithmetic problems involving ingredient mixes. This rule allows us to calculate the ratio in which two or more elements at the same price must be blended to obtain the desired price mixture.

Rule Of Alligation

Let’s understand the important formulas for Mixture and Alligation!

Assume that two components with concentrations of ‘a’ and ‘b’ have been blended in a certain proportion. Let’s call ‘a’ the less expensive component and ‘b’ the more expensive component. One alligation rule states the following:

[Quantity of less expensive substance/Quantity of more expensive substance] = [(C.P. of more expensive substance) – (Mean price)/(Mean price) – (C.P. of less expensive substance)] = [(C.P. of more expensive substance) – (Mean price)

Let’s say ‘c’ is the cost price or C.P. of a unit quantity of a cheaper substance,’m’ is the mean price, and ‘d’ is the cost price of a unit quantity of a more expensive material.

(Quantity of the Less Expensive Substance): (Quantity of the More Expensive Substance) = (d – m): (m – c).

 Let’s look at an example to gain further insights.

Example 1: To make a mixture of Rs. 10, how much rice at Rs. 9.30 per kg must be mixed with rice at Rs. 10.80 per kg?

Answer: Using the alligation rule, we get:

1 kilogramme rice C.P. (in paise) = 1080 paise = d

Furthermore, the C.P. of 1 kg 2nd kind rice (in paise) = 930 paise = c

Also, the average price of the mixture (in paise per kg), or m = 1000 paise. As a result of the alligation rule, we have:

(Quantity of Cheaper Rice) = (1080 – 1000)/(1000 – 930). (Quantity of More Expensive Rice) = (1080 – 1000)/(1000 – 930).

As a result, the needed ratio is 80:70 (or 8:7), and the solution is 8:7.

Conclusion

That’s a wrap to the definition of Mixture & Alligation! The concept of Mixture & Alligation allows us to determine the ratio in which two or more elements at a particular price must be combined to achieve the desired price mixture. We also learned all the important formulas of mixture and alligation and their examples.