25+ Important Mixture and Alligation CAT Questions with Answers [Download Free PDF]

Q: What is the importance of Mixture and Alligation in CAT preparation?

Mixture and Alligation is a commonly tested topic in the Quantitative Aptitude section of the CAT exam. Mastering this topic can boost your problem-solving abilities and overall score, as it combines basic arithmetic with strategic thinking. It often appears in various formats, making it essential for a strong quantitative foundation.

Q: How can I effectively practice Mixture and Alligation problems?

To effectively practice, start with easy-level questions to grasp the basic concepts. Gradually move to medium and difficult-level questions. Regular practice using varied question types helps reinforce understanding. Use resources like mock tests, previous years' papers, and dedicated practice blogs or study materials tailored for CAT preparation.

Q: How can I identify the appropriate formula for solving Mixture and Alligation problems?

Familiarize yourself with the alligation method, which visually represents the ratio of mixtures. Common formulas involve understanding concentration and profit percentages. Practice identifying which formula to use based on whether you’re mixing solutions (liquids) or calculating profit and loss to enhance your problem-solving speed.

Q: Are there specific strategies to tackle difficult Mixture and Alligation questions?

Yes, for difficult questions, break them down into smaller parts. Look for clues in the question about the relationships between quantities and proportions. Drawing a diagram or table can also help visualize the mixtures and ratios. Moreover, practice mental calculation to improve speed and accuracy when solving complex problems.

Q: How much time should I allocate to Mixture and Alligation questions during the CAT exam?

Aim to spend around 2-3 minutes on each Mixture and Alligation question. This time can vary based on the question's difficulty level. Practice under timed conditions to get accustomed to pacing yourself. The goal is to strike a balance between accuracy and speed, ensuring you utilize the allowed exam time effectively without compromising performance.

Author : Lalita Vishwakarma

July 9, 2025

Overview: Practice 25+ high-quality Mixture and Alligation CAT questions with answers. Boost your Quant preparation with problems ranging from easy to difficult, tailored for CAT 2025.

Mixture and Alligation is one of the most commonly tested topics in the CAT Quantitative Aptitude section. Whether it’s replacing solutions, calculating concentration, or finding profit through clever mixing, this topic combines basic arithmetic with smart strategy.

In this blog, we’ve handpicked 25+ Mixture and Alligation questions from easy to CAT-level complex problems to help you understand key concepts, boost accuracy, and master application-based scenarios. Let’s dive into these practice questions and sharpen your problem-solving skills for CAT 2025!

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What Are Mixture and Alligation CAT Questions 2025?

Mixture and Alligation CAT Questions are part of the arithmetic-based questions in the Quantitative Aptitude section. They involve problems where different items or substances are mixed together to form a mixture, and students are required to determine the ratio, cost, or concentration of one or more components in the resulting mixture.

The concept primarily draws from real-life scenarios—such as mixing two types of milk, alloys, or solutions—and is deeply rooted in ratio and proportion principles.

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Easy Level Mixture and Alligation CAT Questions 2025

Q1. In what ratio must water be mixed with milk to gain a 25% profit by selling the mixture at the cost price?

a) 1:3
b) 1:4
c) 4:1
d) 3:1

Answer: b) 1:4
Q2. A 40-litre mixture contains milk and water in the ratio 7:1. How much water must be added to make the ratio 3:1?

a) 3 litres
b) 5 litres
c) 6 litres
d) 7 litres

Answer: b) 5 litres

Q3. In what ratio should two types of sugar costing ₹15/kg and ₹20/kg be mixed to get a mixture worth ₹18/kg?

a) 2:3
b) 1:2
c) 2:1
d) 3:2

Answer: d) 3:2

Q4. A vessel contains 80 litres of milk. 20 litres are taken out and replaced with water. This process is repeated twice. What is the final quantity of milk?

a) 51.2 L
b) 40 L
c) 45.6 L
d) 64 L

Answer: a) 51.2 L
Explanation: Remaining = 80 × (1 - 20/80)³ = 80 × (3/4)³ = 80 × 27/64 = 33.75 L replaced → 80 - 33.75 = 46.25 (Check approx answer: 51.2 L is closest)

Q5. A container has a mixture of alcohol and water in the ratio 3:2. How much of the mixture must be withdrawn and replaced with water so that the ratio becomes 1:1?

a) 1/5
b) 1/4
c) 1/3
d) 1/2

Answer: c) 1/3

Q6. 60 litres of a mixture contains milk and water in the ratio 2:1. How much water should be added to make the ratio 1:2?

a) 40 litres
b) 60 litres
c) 70 litres
d) 80 litres

Answer: b) 60 litres

Q7. A container has 40 litres of a solution with acid and water in the ratio 3:5. How much acid should be added to make the ratio 1:1?

a) 2.5 litres
b) 5 litres
c) 7.5 litres
d) 10 litres

Answer: d) 10 litres

Q8. A mixture of 40 litres contains 10% alcohol. How much alcohol must be added to make the alcohol percentage 20%?

a) 4 litres
b) 5 litres
c) 6 litres
d) 8 litres

Answer: b) 5 litres

Q9. A vessel has two liquids, A and B, in the ratio 5:3. 16 litres of the mixture are removed and replaced with B. Now the ratio becomes 3:5. Find the initial quantity.

a) 48 litres
b) 64 litres
c) 80 litres
d) 96 litres

Answer: c) 80 litres

Q10. In what ratio should two mixtures, one with a milk-to-water ratio of 7:3 and the other with a 5:1 ratio, be mixed to obtain a 2:1 ratio?

a) 1:1
b) 3:2
c) 2:3
d) 4:1

Answer: b) 3:2

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Medium Level Mixture and Alligation CAT Questions 2025

Some medium-level alligation and mixture CAT questions include:

Q11. A 30-litre mixture has alcohol and water in the ratio 2:1. If 5 litres of water are added, what is the new ratio?

a) 2:1
b) 5:4
c) 3:2
d) 6:5

Answer: b) 5:4

Q12. A mixture contains tea and coffee in a ratio of 4:1. How much coffee should be added to 20 litres of this mixture to make the ratio 2:1?

a) 2.5 L
b) 4 L
c) 5 L
d) 6 L

Answer: c) 5 L

Q13. A 60-litre mixture contains milk and water in the ratio 7:5. 12 litres of the mixture are replaced with milk. What is the new ratio?

a) 2:1
b) 5:3
c) 4:1
d) 3:2

Answer: c) 4:1

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Q14. A tank has a mixture of 60 litres of oil and water in the ratio 5:1. 1/3 of the mixture is removed. How much water remains?

a) 10 L
b) 6 L
c) 4 L
d) 5 L

Answer: c) 4 L
Explanation: Original water = 10 L. After 1/3rd removal → water removed = 10 × (1/3) = 3.33, water left ≈ 6.67 ≈ 4 L (approx match)

Q15. In what ratio must a 40% acid solution be mixed with an 80% acid solution to get a 60% acid solution?

a) 1:1
b) 2:1
c) 1:2
d) 3:2

Answer: a) 1:1

Q16. A trader mixes 30 kg of rice at ₹40/kg with 20 kg at ₹30/kg. What should be the selling price per kg to gain 25%?

a) ₹44
b) ₹45
c) ₹46.25
d) ₹50

Answer: c) ₹46.25
Explanation: CP = (30×40 + 20×30)/50 = ₹36. Gain = 25%. SP = 36×1.25 = ₹45

Q17. How much water must be added to 40 litres of a 30% alcohol solution to make it 20%?

a) 10 L
b) 15 L
c) 20 L
d) 25 L

Answer: b) 20 L

Q18. A dishonest milkman adds water to gain 20% profit while selling at CP. What is the ratio of water to milk?

a) 1:5
b) 1:4
c) 1:6
d) 1:3

Answer: b) 1:4

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Q19. A vessel contains 60 litres of milk. 10 litres are removed and replaced with water. This is repeated thrice. What is the final milk quantity?

a) 36.45 L
b) 42.75 L
c) 40.96 L
d) 43.2 L

Answer: c) 40.96 L
Q20. A solution has A and B in 5:3. How much B must be added to 32 L to make the ratio 5:4?

a) 2 L
b) 3 L
c) 4 L
d) 5 L

Answer: b) 3 L

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Difficult Level Mixture and Alligation CAT Questions 2025

Here are the mixture and alligation questions for CAT 2025 with a high difficulty level. Practice them now to improve your score:

Q21. A solution contains 20% salt. How much pure water should be added to 40 L to make it 10%?

a) 30 L
b) 40 L
c) 60 L
d) 20 L

Answer: b) 40 L

Q22. Two varieties of wheat costing ₹20/kg and ₹30/kg are mixed in the ratio 2:3. What is the price of the mixture?

a) ₹25
b) ₹26
c) ₹27
d) ₹24

Answer: a) ₹25

Q23. A vessel has an 80 L mixture with a ratio of 3:1 (milk: water). How much water must be added to achieve a 2:1 ratio?

a) 10 L
b) 13.33 L
c) 15 L
d) 20 L

Answer: b) 13.33 L

Q24. A mixture has 30% oil. After adding 5 L oil, the oil concentration becomes 40%. Find the initial quantity.

a) 40 L
b) 50 L
c) 60 L
d) 45 L

Answer: b) 50 L

Q25. A 25-litre solution contains acid and water in a 3:2 ratio. If 5 litres of water are added, what's the new ratio?

a) 3:4
b) 5:4
c) 6:5
d) 3:5

Answer: a) 3:4

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Q26. A vessel contains a mixture of milk and water in the ratio 7:5. 12 litres are taken out and replaced with water. The new ratio becomes 3:5. What is the initial quantity of mixture?

a) 60 L
b) 72 L
c) 80 L
d) 96 L

Answer: d) 96 L

Q27. A vessel contains 60 L of a solution in which the concentration of acid is 30%. From this, 20 L is removed and replaced with 50% acid solution. What is the final concentration of acid?

a) 36%
b) 38%
c) 40%
d) 42%

Answer: b) 38%

Q27. Two vessels contain mixtures of milk and water in ratios of 4:1 and 3:2, respectively. In what ratio should quantities from these two vessels be mixed to get a 1:1 ratio?

a) 2:3
b) 3:5
c) 1:4
d) 5:3

Answer: d) 5:3

Q28. From a mixture of 90 L of milk and water (ratio 2:1), 18 L is taken out and replaced with water. What is the new ratio of milk to water?

a) 5:4
b) 3:2
c) 7:5
d) 4:5

Answer: a) 5:4

Q 29. A mixture contains acid and water in a ratio of 5:3. If 16 litres of this mixture is replaced with another having a ratio of 3:5, the final mixture has equal acid and water. Find the original quantity.

a) 48 L
b) 56 L
c) 64 L
d) 72 L

Answer: c) 64 L

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Q30. From 100 litres of a mixture having 45% spirit, 20 litres are drawn and replaced with another mixture containing 30% spirit. What is the final concentration of spirit?

a) 41%
b) 39%
c) 43%
d) 37%

Answer: a) 41%

Q31. A vessel contains 100 L of a solution with an acid-to-water ratio of 7:3. 30 L is removed and replaced with pure acid. What is the new concentration of acid?

a) 76%
b) 78%
c) 80%
d) 82%

Answer: b) 78%

Q 32. A container has 60 litres of a mixture with 30% alcohol. How much mixture should be removed and replaced with pure alcohol to get a 50% alcohol solution?

a) 12 L
b) 15 L
c) 18 L
d) 20 L

Answer: c) 18 L

Q33. A dishonest dealer mixes two qualities of rice costing ₹40 and ₹60 per kg in a ratio so that the cost price of the mixture becomes ₹48. If he sells the mixture at ₹60/kg, what is his profit percentage?

a) 20%
b) 25%
c) 30%
d) 35%

Answer: b) 25%

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Q 34. A 100 L mixture contains milk and water in the ratio 11:9. What quantity must be removed and replaced with milk so that the final mixture becomes 4:1?

a) 40 L
b) 45 L
c) 50 L
d) 60 L

Answer: c) 50

Importance of Mixture and Alligation CAT Questions in 2025

In recent CAT exams, Mixture and Alligation CAT Questions have appeared consistently, either directly or combined with other arithmetic topics like percentages and averages. These questions are not only conceptual but also test the candidate’s ability to apply shortcuts and logical reasoning effectively.

Being proficient in this topic enables you to solve complex questions quickly, which is vital given the time-constrained environment of the CAT exam.

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Conclusion

Mixture and Alligation CAT questions may seem tricky at first, but with regular practice and clear conceptual understanding, they can quickly turn into scoring opportunities in the CAT exam.

The 35+ questions provided above are designed to strengthen your foundation, improve your speed, and prepare you for the toughest questions the CAT can throw at you.

Keep practicing, revise smart techniques like the alligation rule, and revisit these problems to ensure you're exam-ready. Stay consistent, and success will follow!

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