50+ Mixture and Alligation Questions and Answers | Free Online Quiz for SSC, Banks, Other Exams

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mixture and alligation

Mixture and Alligation – Concept, Formulas, Tricks, and Questions

Mixture and Alligation is an important topic in quantitative aptitude for exams like SSC, Bank PO, Railway, CAT, and campus placements.

These problems deal with mixing two or more ingredients with different prices or quantities to find the average price or ratio of mixture.

Understanding the Alligation rule makes these questions much easier.

In this guide, you will learn:

  • Mixture and Alligation concept
  • Important formulas
  • Alligation rule
  • Solved examples
  • Practice questions

Mixture and Alligation Online Quiz
Mixture and Alligation Quiz 1 Mixture and Alligation Quiz 2(Inactive) Mixture and Alligation Quiz 3(Inactive)

What is Mixture and Alligation?

A mixture refers to combining two or more ingredients together.

Alligation is a rule used to determine the ratio in which ingredients should be mixed to get a desired average value.

It is commonly used in problems involving:

  • prices of commodities
  • concentration of liquids
  • mixing different qualities.

Related Aptitude Topics

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Mixture and Alligation for Competitive Exams

This topic frequently appears in:

Understanding this topic helps solve many ratio and average problems quickly.

Important Mixture and Alligation Formula

To solve any numerical ability question, candidates must be familiar with a set of formulae for each topic, which makes the process easier and saves time. Here are a few formulas to assist candidates in handling mixture and alligation questions more easily:

The basic formula for calculating the ratio in which the materials are blended is

Mixture and Alligation
It is also known as the rule of alligation and can be expressed as

Mixture and Alligation

Tips to Solve Mixture and Alligation Questions Faster

Follow these exam tips:

  • Use the Alligation rule
  • Apply cross difference method
  • Use weighted averages
  • Practice previous exam questions
  • Avoid complex calculations

Most mixture problems can be solved in under 30 seconds with practice.

Mixture and Alligation Questions

Q1.There are two types of sugar. One is priced at Rs 62 per kg and the other is priced at Rs 72 per kg. If the two types are mixed together, the price of new mixture will be Rs 64.50 per kg. Find the ratio of the two types of sugar in this new mixture.

  1. 2:5
  2. 3:1
  3. 6:7
  4. 3:2
  5. None

Explanation:

Cost Price of 1kg of Type 1 sugar = 6200 p.
Cost Price of 1kg of Type 2 sugar = 7200 p.
Mean Price of 1 kg of mixture = 6450 p.
According to the Rule of Alligation,
(Quantity of Cheaper):(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper)
Therefore, the required ratio = (7200-6450):(6450-6200) = 750:250 = 3:1.

Q2. A certain quantity of water is mixed with milk priced at Rs 12 per litre. The price of mixture is Rs 8 per litre. Find out the ratio of water and milk in the new mixture.

  1. 3:2
  2. 1:2
  3. 5:2
  4. 2:1
  5. None of these

Explanation:

Cost Price of 1 litre of water = Rs 0.
Cost Price of 1 litre of milk = Rs 12.
Mean Price of Mixture = Rs 8.
According to the Rule of Alligation,
(Quantity of Cheaper) :(Quantity of Dearer) = (CP of dearer – Mean Price):(Mean Price – CP of cheaper)
Therefore, Water : Milk = (12-8):(8-0) = 4:8 = 1:2.

Q3. A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo? In the zoo, each horse had four legs and each pigeon had two legs.

  1. 40
  2. 30
  3. 50
  4. 60
  5. None of these

Explanation:

Let the number of horses = x
Then the number of pigeons = 80 – x.
Each pigeon has 2 legs and each horse has 4 legs.
Therefore, total number of legs = 4x + 2(80-x) = 260
4x + 160 – 2x = 260
2x = 100
x = 50.

Q4. An alloy contains a mixture of Zinc, Copper and Iron in the ratio of 4 : 5 : 7. If 24 kg of mixture is taken out and 5 kg of Zinc and 12 kg of Iron is mixed in the alloy. In the resultant mixture quantity of Iron is 26 kg more than Copper, then what is total quantity of initial mixtures?

  1. 106 kg
  2. 112 kg
  3. 121 kg
  4. 136 kg
  5. none of these

Explanation:

Let after 24 kg of alloy is taken out, the quantity of Zinc, Copper, and Iron be 4x, 5x and 7x kg respectively.
According to question
(7x + 12) – 5x = 26
Therefore, x = 7
∴ Total quantity of initial alloy = 24 + (4x + 5x + 7x) = 24 + 16 × 7= 136 kg.

Q5. A vessel of 80 l is filled with milk and water in parts separately. 75% of milk and 25% of water is taken out of the vessel. It is found that the vessel is vacated by 60%. Find the initial quantity of water.

  1. 24 litres
  2. 27 litres
  3. 32 litres
  4. 36 litres
  5. 40 litres

Explanation:

Let the initial volume of water be ‘w’ litres and the volume of milk = ‘m’ litres
m + w = 80
On removing 75% of milk and 25% of water from the vessel,
0.25m + 0.75w = 80 * 0.4 = 32
= m + 3w = 128
Using the pairs of equations, m = 56, w = 24

Q6.  Two vessels A and B contain mixtures of milk and water in the ratios 3 : 7 and 4 : 1 respectively. In a third vessel C, in what ratio should quantities of mixture be taken from vessels A and B are mixed to form a mixture in which ratio of milk and water is 7 : 9?

  1. 3 : 5
  2. 7 : 8
  3. 11 : 9
  4. 11 : 28
  5. None of these

Explanation:

Using the rule of Alligation, we get

mixture and alligation

= A : B = 29 : 11

Q7.  A mixture of milk and water in a jar contains 29 Liters milk and 9 Liters water. To this mixture, Y Liters milk and Y Liters water are added. If 60% of the new mixture is 36 L, then find the value of Y.

  1. 7 Litres
  2. 11 Litres
  3. 13 Litres
  4. 15 Litres
  5. None of these

Explanation: 

According to the question,

60% of new mixture = 36 L

100% of new mixture = (36/60) × 100 = 60 L

i.e., 29 + 9 + Y + Y = 60

⇒ Y = 22/2 = 11 L

Q8. A mixture of milk and water containing 40 liters of water and y liters of milk. If 50 liters milk is added to the mixture. Then the ratio of milk and water in the resultant mixture become 3:2. Then find the value of y?

  1. 5 liters
  2. 15 liters
  3. 25 liters
  4. 10 liters
  5. 20 liters

Explanation:

mixture and alligation

The questions above will help you understand how to answer Mixture and alligation questions, as well as the kind of questions that may be asked about this topic. ⁤

Mixture and Alligation is an important topic in quantitative aptitude. Understanding the alligation rule, formulas, and shortcuts allows you to solve problems quickly.

Regular practice and concept clarity will help you perform well in SSC, Bank, Railway, and other competitive exams.

Frequently Asked Questions (FAQs)

1. What is Mixture and Alligation in aptitude?

Mixture and Alligation is a quantitative aptitude topic used to determine the ratio in which two or more ingredients must be mixed to obtain a desired average value. These problems commonly appear in competitive exams like SSC, bank, and railway exams.

2. What is the Alligation rule?

The Alligation rule is a mathematical method used to find the ratio in which two quantities with different values must be mixed to get a mixture with a desired mean value. Formula: Ratio of quantities = (Dearer Price − Mean Price) : (Mean Price − Cheaper Price)

3. How do you solve Mixture and Alligation questions quickly?

Mixture and Alligation questions can be solved quickly using: the Alligation rule the cross difference method the weighted average method These methods simplify calculations and help solve questions faster during exams.

4. What is the difference between mixture and alligation?

A mixture refers to combining two or more substances together. Alligation is the rule used to determine the ratio in which those substances must be mixed to achieve a specific average value.

5. Why are Mixture and Alligation questions important for competitive exams?

Mixture and Alligation questions are frequently asked in exams such as: SSC CGL SSC CHSL Bank PO Bank Clerk Railway exams They test a candidate’s ability to calculate ratios, averages, and percentages quickly.

6. What types of problems are included in Mixture and Alligation?

Common types of mixture and alligation problems include: mixing commodities with different prices mixing liquids with different concentrations milk and water mixture problems profit and loss mixture problems