Prakhar Gupta has 4+ years of experience in Content Marketing Field. 

Content Marketing Specialist

Today in our blog, we are going to learn questions related to mixtures with the use of alligation in the Quantitative Aptitude Section.

Mixture: The new product obtained by mixing two or more ingredients in a certain ratio is called a mixture or combination of two or more quantities is known as a mixture. A mixture has two types: When two different ingredients are mixed together it is called a simple mixture and when two or more simple mixtures are mixed together, it is called a compound mixture.

Let’s discuss some examples of mixture: Water and milk, water and pure spirit, the weight of boys and girls in a classroom, Kerosene and petrol, etc.

Mean price: The cost price of a unit quantity of the mixture is called the mean price. It will always be higher than the cost price of cheaper quantity and lower than the cost price of dearer quantity.

<h2>Weighted average mothod</h2>

E.g. The average weight of a class of 40 students is 30 and the average weight of the class of 20 students is 15. Find the average weight of both the combined classes? Sol: By the concepts of averages, The required average = (40 × 30 + 20 × 15)/(40 + 20) = (1200 + 300)/60 = 1500/60 = 25 (Ans.)

E.g. 16 liters of kerosene is mixed with 5 liters of petrol. The price of kerosene is rs.12 per liter and the price of petrol is rs. 33 per liter. The average price of the mixture per liter is? Sol: By the concepts of average, The required average = (16 × 12 + 5 × 33) / (16 + 5) = (192 + 165) / 21 = 357 / 21 = 17 (Ans.)

<h2>Alligations</h2>

The literal meaning of alligation is ‘linking’. The Alligation rule states that "When different quantities of same or different ingredients, of different cost(value), are mixed together to produce a mean cost(value), the ratio of their quantities are inversely proportional to the difference of their cost from the mean(cost) price."

(Quantity of cheaper cost ingredient) / (Quantity of dearer cost ingredient) = (dearer cost - Mean cost) / (Mean cost - cheaper cost)

or q1 / q2 = (C2 - Cm ) / (Cm - C1 )

Where, q1 = Quantity of cheaper cost ingredient q2 = Quantity of dearer cost ingredient C1 = Cost price of cheaper cost ingredient C2 =Cost price of dearer cost ingredient Cm = Cost price of the mixture(mean price)

Diagram Representation:

<img loading="lazy" alt=" Alligation diagram representation" src="https://study.kdcampus.live/admin/assets/uploads/ckeditor/Alligation diagram representation.webp" style="height:150px; width:221px" />

E.g. The average weight of the class of 40 students is 30 and the average weight of the clas s of 20 students is 15. Find the average weight of both the combined classes?

Sol: Alligation method:

<img loading="lazy" alt=" Alligation example diagram representation" src="https://study.kdcampus.live/admin/assets/uploads/ckeditor/Alligation example diagram representation.webp" style="height:150px; width:172px" />

In the graphical representation of the solution, x is the weighted average where 15 and 30 are the averages of different classes. Now, the difference between the two averages is divided in the inverse ratio of the quantities written below, so according to the problem difference (15) will be divided in the ratio 2 : 1 = 40 : 20 So, the value of x = 15 + 2/3 × (30 - 15) = 25 (Ans.)

E.g. 16 Litres of kerosene is mixed with 5 liters of petrol. The price of kerosene is Rs.12 per liter and the price of petrol is Rs.33 per liter. The average price of the mixture per liter is: Sol: Alligation method:

The difference of 33 and 12 be divided in the ratio of 16 : 5 ⇒ 33 - 12 = 21 Again, on dividing 21 in the ratio 16 : 5, we get first part = 5 and second part = 16. The average price 12 + 5 = 17 (Ans.)

E.g. In what proportion must a grocer mix teas of Rs.1.02 per kg and Rs.1.44 per kg so as to make a mixture worth Rs.1.26 per kg? Sol: As per alligation rule: ⇒ q1 /q2 = (1.44 - 1.26)/(1.26 - 1.02) (As per alligation) ⇒ (0.18)/(0.24) = 3/4 (Ans.)

E.g. A container contains 40 L of milk. From this container, 4 L of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now there in the container? Sol: Original quantity of milk = 40L Since 4L of milk is taken out Quantity of the new mixture would be 40 - 4 = 36L Now, when 4L of the mixture is taken out, Quantity of milk taken out = 4 × 36 / 40 = 3.6L Quantity of milk left = 36 - 3.6 = 32.4L Similarly taken out in the third step: 4 × 32.4 / 40 = 3.24L Quantity of milk left = 32.40 - 3.24 = 29.16L (Ans.)

This was a really long method. Let’s discuss a short trick, If a container initially contains ‘a’ unit of liquid and ‘b’ unit of liquid is taken out and it is filled with ‘b’ unit of another liquid, then after n operations, the final quantity of the original liquid in the container is given as:

[a(1 - b/a)n ] Units

E.g. A container contains 40 L of milk. From this container, 4 L of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now there in the container? Sol: a = 40, b = 4, n = 3 So according to the formula, 40(1 - 4/40)3 = 40(1 - 1/10)3 = 40(9/10)3 = 40 × 729/1000 = 29.16 L (Ans.)

Alligation rule for a mixture of three ingredients:

When three ingredients of quantity q1 , q2 and q3 and cost prices C1 , C2 and C3 are mixed, and the mean cost price (mean price) is Cm then q1 : q2 : q3 = (C2 - Cm )×(C3 - Cm ):(Cm - C1 )×(C3 - Cm ):(C2 - Cm) × (Cm - C1 )

We learned the concept of alligation which is a surgical strike for mixtures questions, so practice questions by alligation method because it is quick and precise too. Stay in touch for more.

Since 1995, Neetu Mam is Providing Free Content for English to the Students

Best Publisher for English Content

Learn the key concepts of mixtures and alligations

Mixtures and Alligations - Quant Study Notes for Competitive Exams

प्रतियोगी परीक्षाओं के लिए मात्रात्मक योग्यता - मिश्रण और गठबंधन

Latest Notifications

Exam Eligibility

Exam Dates

Exam Pattern

Syllabus

Admit Card

Exam Cutoff

Answer Key

Exam Results

Daily Current Affairs

Current Affairs Quiz

Daily Editorial

Daily Vocabulary

Study Plan

Important Days

Question Paper

Previous Year PDF

English Language

Logical Reasoning

Quantitative Aptitude

General Knowledge

General Awareness

General Science

Today in History

Know Your State

Full Form

Know Your Country

Government Schemes

Know Your City

Know Your Leader

Books and Authors

question answer

Quiz

Courses

Classes

Quant Tricks for SSC CGL Exam

&lt;p&gt;No title&lt;/p&gt;

Quant Important Topics for SSC CGL Exam

No title

Click to study the Complete Theory of mixtures and alligations  and practice a lot of questions difficulty wise that can be asked in your competitive exam.

Mixtures and Alligations - Quant Study Notes for Competitive Exams

Mixtures and Alligations FAQs

What is a mixture?

What are two types of mixtures?

What the Alligation rule states?

What is the concept of mean price?

Tell about the Alligation rule for a mixture of three ingredients.

Mixtures and Alligations Comments:

Mixtures and Alligations RELATED ARTICLES