CAT 2022 : Alligations and Mixtures – Formulas and Tricks

In this article, we will take a recap of all the important formulas, tricks and shortcuts that will help you solve questions easily within less time.

1. A Mixture is a result of the mixing of two or more ingredients in some fixed ratio(or quantity) and a combination of two mixtures is also called a Mixture.

2. Alligation is a process of linking or we can say that the process of mixing the two quantities of different ingredients or different costs to form a mixture of mean cost.

3. Concept of weighted average:

Weighted average =

If x₁ quantity is sold for Rs a₁ per kg, x₂ is sold for Rs a₂ per kg, x₃ quantity is sold for Rs a₃ per kg and so on x_n quantity is sold for Rs a_n per kg respectively, then the weighted average ‘w’ is given by:

4. Alligation Rule:

Suppose Rs. d per unit be the price of the first ingredient (superior quality) mixed with another ingredient (cheaper quality) of price Rs. c per unit to form a mixture whose mean price is Rs. m per unit, then the two ingredients must be mixed in the ratio:

i.e., the two ingredients are to be mixed in the inverse ratio of the difference of their prices and the mean price.

5. If a vessel has ‘y’ units of mixture of ingredients ‘a’ and ‘b’. From this mixture ‘x’ unit is taken out and replaced by an equal amount of ingredient b.This process of taking out and replacing is repeated say for ‘n’ times. Then,

Amount of ‘a’ left in the mixture = Total mixture x 

6. When we have questions containing water, we consider value of water as zero. (Though it is priceless J)
   1. A mixture of a certain quantity of milk and ‘z’ litres of water is worth Rs ‘a’per litre. If pure milk is worth Rs ‘b’ per litre, then the quantity of milk is given by .
   2. In what ratio water must be mixed with spirit to gain or to lose x% by sellingit at cost price is given by ()

Alligations and Mixtures Questions: Problems on Alligations and Mixtures you should solve for competitive examination preparation

Welcome to this exercise on Problems on Alligations and Mixtures. In this exercise, we look at the summary of tips and tricks for Alligations and Mixtures. As you prepare for your competitive examinations, you will come across questions on Alligations and Mixtures. Such questions need optimized tackling and can be solved with ease by using simple tricks and understanding the relationships highlighted in this Alligations and Mixtures Questions article. The Alligations and Mixtures Questions exercise comes into the picture where it gives you a chance to practice the highlighted and important concepts related to Alligations and Mixtures question type.