30+ Mixture and Alligation CAT Questions with Solutions [PDF Download]

Overview: Mixture and Alligation CAT questions frequently test your ability to solve real-life problems involving ratios, proportions, and concentrations. This topic is a favourite of examiners due to its practical applications in daily life and its flexibility in problem formulation. 

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Key Takeaways

• Understand the core principles of Mixture and Alligation, including ratios, proportions, and concentration.
• Learn how to solve real-life problems involving mixtures of different quantities, costs, or concentrations.
• Get familiar with shortcuts and tricks to solve these problems faster and more efficiently.
• Improve your speed and accuracy in handling time-sensitive questions in the CAT exam.

What You Will Learn in This Blog: Sample Mixture and Alligation questions to practice +Concepts and formulas used in Mixture and Alligation problems.

What Are Mixture and Alligation CAT Questions 2026?

Mixture and Alligation CAT Questions are part of the arithmetic-based questions in the Quantitative Aptitude section of the CAT syllabus. These problems involve mixing different items or substances 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 the principles of ratio and proportion.

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Easy Level Mixture and Alligation CAT Questions 2026

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)

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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

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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

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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 2026

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

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)

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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 2026

Here are the mixture and alligation questions for CAT 2026 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

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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 varieties of rice, costing ₹40 and ₹60 per kg, in a ratio so that the cost price of the mixture is ₹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 

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Importance of Mixture and Alligation CAT Questions in 2026

In recent CAT exams, Average 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.

Preparation Tips for Mixture and Alligation CAT Questions

1. Start with the basics

Before diving into shortcuts, make sure you understand the core concepts behind CAT Mixture and Alligation Questions, such as averages, ratios, and percentage compositions. Try solving a few problems using traditional methods to strengthen your fundamentals.

2. Master the alligation method

Once you're comfortable with the basics, learn the alligation "cross" technique. It’s a powerful shortcut that can save time in solving Mixture and Alligation CAT Questions, especially those involving price, concentration, or replacement.

3. Practice smart and track progress

Regularly solve a variety of CAT Mixture and Alligation Questions from previous papers and mock tests. Focus on speed, accuracy, and spotting common patterns. Reviewing your mistakes and keeping a quick revision sheet of key formulas will also boost your performance.

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Conclusion

CAT Mixture and Alligation questions 2026 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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