Average, Mixture and Alligation for SSC and Railways Exams

By : Neha Uppal

Updated : Nov 9, 2020, 13:02

Average, Mixture and Alligation questions are often asked in competitive exams like RRB NTPC, RRB/RRC Group D exam, SSC CGL, SSC CHSL, SSC MTS, SSC Junior Engineer, RRB JE, etc. It is important to understand the Average, Mixture, and Alligation concepts in a comprehensive manner and also learn the best way to prepare and practice the topic for a better score in the exam.

The ‘Alligation’ is an important topic for quantitative aptitude questions in competitive exams. It helps us in finding the ratio in which two mixtures must be mixed to produce a final mixture at a given price. Alligation is used in a lot of areas like profit and loss, S.I (Simple Interest), time and distance, etc. The price of the mixtures that are to be mixed are given to us, and we have to find the solution.

Important Average, Mixture and Alligation Topics



Rule of Alligation

If two ingredients namely ‘a’ and ‘b’ are mixed with ‘a’ as a cheaper ingredient and ‘b’ is the dearer/costly ingredient, then the average mixture alligation formula is:

Quantity of a/Quantity of b = (Cost of b – Mean Price) / (Mean Price – Cost of a)

Mean Price

The cost of the unit quantity of the final mixture is called the mean price.

Method of Repeated Dilutions

Suppose ‘x’ is the unit of liquid present in any container and we take out ‘y’ units of liquid from that container and replace it with water or some other liquid. In that case, the quantity of pure liquid in that container after n times we repeated the process is:

[x (1 – (y/n)] n

Percentage-wise Mixtures

If a question states some mixture with a particular percentage of an ingredient ‘a’ in it and we are asked how much more ‘a’ is to added in the mixture to make the percentage of ‘a’ in mixture as given, then,

Total Mixture (required % of a - present % of a) / (100 – required % of a)

Tips to Solve/Prepare Mixture and Alligation Questions

  • Make sure you know how to find the ratio of three mixtures if they are mixed to achieve a particular mean price. If a, b, and c are the price of mixtures to be mixed to achieve a final mean price ‘m’. Then apply the alligation and mixture formula on the first and third ingredient (1) and on the second and third ingredient (2). The ratio of the first and second ingredient will be found, and the add the ratios of the third ingredient in both the step (1) and (2), which will be the ratio of the third ingredient in the final mixture. You can download the alligation and mixture formula pdf from the internet.
  • Make sure to read the question before you solve it, sometimes alligation questions may be confusing because the mixtures can be replaced by speed, profit and loss, etc.
  • Sometimes you may be asked the ratio of original ingredients and the ratio of the final mixture will be given. Apply the Average, Mixture, and Alligation method and find out.

Importance of Alligation and Mixture in Quantitative Section of Competitive SSC and Railways Government Exams

  • Quantitative section is a different section in SSC and railways exams, and alligation and mixture is an important concept of the quantitative section.
  • It is almost compulsory that you will be asked alligation and mixture questions in SSC and railways government exams. This topic has never been left out in all the previous year exams.
  • It is a diverse topic from which questions can be made on profit and loss, speed, percentage problems, etc. which highlights its importance.
  • Average mixture and alligation questions test a lot of things like quantitative analysis, numerology skills, etc. which highlights its importance.

Most Recommended Books for Alligation and Mixture



R.S Agarwal – Quantitative Aptitude for Competitive Examinations

R.S Agarwal

Arun Sharma – Quantitative Aptitude

Arun Sharma

Arihant Publications – Fast Track Objective Arithmetic

Rajesh Verma

R.D Sharma – Mathematics

R.D Sharma

Why Prepare Alligation and Mixture from BYJU'S Exam Prep?

BYJU'S Exam Prep provides you with a personalised learning platform. It is widely preferred for SSC and railway exams. BYJU'S Exam Prep also provides you with practice papers that will hone your quantitative analysis skills. The online test series and average mixtures and alligations quiz conducted by BYJU'S Exam Prep will help you in testing yourself and finding the shortcomings. The online classes of BYJU'S Exam Prep are also well oriented. It is India’s largest preparation site for SSC and Railway exams. The BYJU'S Exam Prep community is free to join where students help each other, and you will find fruitful discussions that will help you in preparing for the exams.

Studying for a competitive exam is a stressful and challenging task, but with the right tips, guidance and supplies, you can achieve your desired result. We hope you found this article is helpful.

Frequently Asked Questions about Average, Mixture and Alligation questions

1- How many questions should one practice?

One must practice as many questions as he/she can because more practice will help you in solving questions faster. You can download the average mixtures and alligations pdf for practising. You can get alligation and mixture notes from BYJU'S Exam Prep.

2- Are there any short tricks for alligation and mixture questions?

Yes, you can learn more about alligation and mixture tricks used to solve questions quickly by BYJU'S Exam Prep online classes.

3- Is there any specific online course for SSC CGL?

Yes, there are specific courses on BYJU'S Exam Prep for SSC CGL, SSC CHSL, SSC CPO, etc. You will also get alligation and mixture question answers with solution SSC via these courses.

4- How to study Average, Mixture, Alligation for competitive exams?

You must understand the concepts of it and then proceed to solve last years’ papers as a form of practice.

5- Which book is the most preferred to study Average, Mixture, Alligation?

R.S Agarwal’s book: R.S Agarwal – Quantitative Aptitude for Competitive Examinations, is considered to be the most straightforward yet advanced book to study for competitive exams.