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Alligation and Mixture Concepts and Formulas

Points to remember:

1. Alligation: It refers to a rule that helps to find the ratio in which two or more ingredients at a given price are mixed to produce a mixture of specified price.
2. Mean Price: It is the cost price of a unit quantity of a mixture which is prepared by mixing two or more ingredients.
3. Alligation rule: It says that if two ingredients at a given price are mixed to produce a mixture at the given price, the ratio of quantity of cheaper ingredient and quantity of dearer ingredient is given by;

Cheaper quantity: Dearer quantity: (d-m) 🙁 m-c)

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Some quicker methods:

1) A container contains x units of a liquid from which y units are taken out and replaced by water. Again from this mixture y units are taken out and replaced by water. If this process is repeated n times;

Or,

Quantity of pure liquid after n operation =

2) If n containers of equal capacity are filled with the mixture of liquids X and Y in the ratio x1: y₁, x₂: y₂,…. x_n: y_n, respectively and the content of all the containers is mixed in a single container;

3) If n containers of different sizes (z₁, z₂,… zn) are filled with a mixture of liquids X and Y in the ratio x₁: y₁, x₂: y₂,…x_n: y_n, respectively and the content of all the containers is mixed in a single container;

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Alligation and Mixture Aptitude Test Paper 1 Alligation and Mixture Aptitude Test Paper 2

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