SSC Maths Mixture and Alligation: Formulas, Tricks, Solved Questions [PDF]

By BYJU'S Exam Prep

Updated on: September 25th, 2023

SSC Maths Mixture and Alligation: Mixture and Alligation topic plays a crucial role in SSC exams. It deals with the concept of combining different components or substances with varying concentrations to achieve a desired mixture. This topic tests a candidate’s ability to solve problems related to proportions, ratios, and the distribution of ingredients. Understanding the principles and techniques of Mixture and Alligation is essential for effectively solving complex mathematical problems in a time-bound manner.

In this article, we have discussed the concepts, formulas, and problem-solving strategies related to SSC Maths Mixture and Alligation, providing you with the necessary knowledge and skills to tackle such questions with confidence. You can also download the SSC Maths Mixture and Alligation Questions PDF for your ease.

SSC Maths Mixture and Alligation

Mixture: A mixture is a mix formed by combining two or more things or substances in a specific ratio or proportion. Mixtures are typically formed by combining solids, liquids, or gases with other solids, liquids, or gases. A mixture, on the other hand, can be created by combining any combination of solids, liquids, and gases.

Types of mixtures are as follows:

  • Simple mixture: A mixture that is formed by combining two or more separate elements.
  • Complex mixture: A mixture formed by combining two or more separate mixtures.

Alligation: Alligation is a rule that assists us in solving difficulties involving mixes. The alligation rule is useful in determining the ratio in which two things or ingredients of a specific cost must be blended to produce a final mixture with elements in a known ratio.

Mixture and Alligation Formula

To answer any numerical ability question, candidates must be familiar with a set of formulae for each topic, which makes answering the questions easier and saves time. Here are a few formulas to help candidates with this and make it easier for them to solve combination and alligation questions.

When gradients are mixed in a certain ratio:


Rule of Alligation:

image002Then, (cheaper quantity) : (dearer quantity) = (d – m ) : (m – c)

Also, check out:

Mixture and Alligation Tricks

The competitive exam is entirely centred on time management to answer the questions correctly. Time management is critical for scoring higher and attempting more questions in less time. Some combination and allegation techniques and methods will help you solve word problems in a matter of minutes. Candidates must use tricks to solve the tasks. Candidates should keep in mind that any tip or trick will be effective only if the candidate applies it frequently. Some of the important tricks to solve one of the most crucial topics of the SSC syllabus for maths are as follows:

  • The rule of alligation can also be used to handle problems involving partnerships, time, work and wages. 
  • Read a question and try to solve it by putting the values in the above-mentioned alligation rule.
  • Questions from this area may appear difficult at first, but they are simple to solve after a candidate understands the concept and the key formulas utilised.
  • Using the alligation rule, you can not only calculate the ratio between the quantities of two elements but also the rate at which the article can be sold.

50 Mixture and Alligation Questions

We have provided below 50 mixture and alligation questions that are important for competitive exams like SSC CGL, SSC CHSL, CPO, MTS, etc.

1. The number of students in a class is 210, out of which 33(1/3)% are boys and the rest are girls. The average score in Science of the boys is 66(2/3)% more than that of the girls. 66 is the average score of all the students then what would be the average score of the girls?

A. 52
B. 54
C. 58
D. 60

Answer ||| B

2. There are 4 sections A ,B ,C and D of class XII in a school. Students in grades A, B, C, and D had average marks of 54%, 58%, 52%, and 70%, respectively. If the average marks of the students of sections A and B together is 55%, the average marks of the students of sections A and C together 53width=7% and that of the students of C and D together is 60%. What is the ratio of the average marks of the students in three sections A, B and C to the average marks of the students in 3 sections B, C and D?

A. width=53 width=55
B. width=53 : width=55
C. width=53 : width=55
D. None of these

Answer ||| C

3. In a mixture of 90 liters of petrol and kerosene, 20% is kerosene. How much more kerosene must be added to the mixture so that the kerosene become 25% of the new mixture?

A. 5 liters
B. 6 liters
C. 8 liters
D. 10 liters
E. None of these

Answer ||| B

4. Solution is 10% acid, while Solution is 30% acid. In what ratio should solution A be mixed with Solution B to obtain a mixture with 25% acid?

A. 1 : 2
B. 3 : 1
C. 1 : 3
D. 2 : 1

Answer ||| C 

5. Two types of tea costing 180/kg and 280/kg should be mixed in the ratio so that the mixture obtained sold at 320/kg. to earn a profit of 20% is?

A. 4 : 13
B. 2 : 13
C. 3 : 13
D. 13 : 2

Answer ||| B 

6.The ratio in which two sugar solutions of the concentrations 25% and 40% are to be mixed to get a solution of concentration 30% is:

A. 4 : 1
B. 3 : 2
C. 2 : 1
D. 9 : 8

Answer ||| C 

7. A solution contains petrol and kerosene in the ratio 5 : 7 respectively. If 42 liters of the solution have been replaced with petrol to create a ratio of 7 : 5. Find out the original amount of kerosene in the solution.

A. 87.5 liters
B. 84 liters
C. 70 liters
D. 85.75 liters

Answer ||| D

8. In an alloy, 24 grams of zinc is mixed with 72 grams of copper. X gram of total mixture is taken out and 16 gm of zinc and 24 gm of copper are added. The final mixture has 70% copper. Determine the amount of the mixture extracted from the alloy.

A. 12 gm
B. 10 gm
C. 16 gm
D. 18 gm

Answer ||| C 

9. A vessel is filled with liquid containing a mixture of 5 part water and 7 part syrup. What percentage of the liquid must be drawn off and replaced with water so that mixture may be half water & half syrup.

A. 14%
B. 16width=7%
C. 14.28%
D. 11%

Answer ||| C

10. Babulal runs a juice corner outside a park and sells giloy juice (giloy+ water) in the morning. Initially, he had 19 litres juice, which had giloy and water in the ratio 2 : 9. He sold width=27 litres juice. Later, in order to dilute it, he added some water and the ratio of giloy and water became 1 : 5. How much water was added?

A. width=26 litres
B. width=16 litre
C. 2 litres
D. 1 litre

Answer ||| A

11. A dealer had 120 kg of wheat. A part of it was sold by him at 10% gain and the rest at 25% gain. overall, he had a gain of 15%. How much of the wheat was sold at 10% gain?

A. 80 kg
B. 60 kg
C. 40 kg
D. 50 kg

Answer ||| A 

12. If 80 liters of a milk solution has 60% milk in it, then how much milk should be added to make the concentration of milk 80% in the solution?

A. 80 liters
B. 65 liters
C. 60 liters
D. 75 liters

Answer ||| A 

13. There are two mixtures A and B having milk and water in ratio 3:1 and 7:5 respectively. The milkman mixes these two mixtures in 2:3 ratio and sells the resultant mixture at the rate of 1 litre pure milk. If on selling 1 litre of mixture A for price of 1 litre of pure milk he gains Rs.14.50. Then find profit he makes on selling 1 litre of resultant mixture at the price of 1 litre pure milk.

A. Rs. 20.3
B. Rs. 30
C. Rs. 15.5
D. Rs. 16.2

Answer ||| A

SSC CGL Mixture and Alligation

Mixture and Alligation is an important concept in the quantitative aptitude section of SSC CGL exam. Based on the analysis of SSC CGL previous question papers, approximately 3-4 questions are dedicated to this topic. It is crucial for SSC CGL aspirants to extensively study and practice Alligation questions to strengthen their problem-solving skills related to proportions, ratios, and ingredient distribution. Moreover, the revised SSC CGL syllabus includes Mixture and Alligation in both Tier 1 and Tier 2 examinations.

Besides this topic, the following topics are also included in the quantitative aptitude section of both tier 1 and 2.

SSC Mixture and Alligation Questions PDF

The questions presented here are only examples of mixture and alligation questions. Candidates must complete more of them to gain a better understanding of the subject by referring to the SSC mixture and alligation questions PDF provided below:

SSC Mixture and Alligation Questions PDF (Click Here)

To get a better understanding of SSC Maths Mixture and Alligation, you can also watch live videos on this topic by joining our SSC Online Coaching Classes and attempting free SSC CGL Mock test series.

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