300+ Most Important Arithmetic Questions for CAT
Alligation Mixture
Alligation & Mixture is a uniquely strategic topic in Arithmetic for CAT 2026, known for its application across pricing, concentration, and ratio-based problems in CAT Quant. Practice curated CAT arithmetic important questions built around the alligation rule, mixture replacement, and multi-component blending problems aligned with recent CAT exam patterns. These questions improve both speed and accuracy in solving non-trivial Quant problems.
Arithmetic
Q1. Danish bought a 2000 ml bottle of Pepsi and drank 5% of it on the first day and replaced it with water. On the second day he drank 10% of the contents and replaced it with water. On the third day he drank 15% and replaced it with water. He continued in this way and drank the whole bottle on the 20th day. Find the average quantity of water (in ml) that Danish drank in these 20 days from the bottle.
Q2. A trader has two coffee-chicory mixtures – A and B – with weights 24 kg and 36 kg, respectively, and they have different prices per kg. Equal quantities of mixtures from A and B are removed. The portion taken from A is mixed with the remaining portion of B, and the portion taken from B is mixed with the remaining portion of A. If both resulting mixtures have the same price per kg, then find the initial quantity (in kg) of mixture removed from each.
16.2
14.4
13.8
15.6
Q3. A chemical is prepared by mixing 120 gm of A, 200 gm of B, and 80 gm of C. The chemist uses 100 gm of this mixture for a lab process and realises that to improve the reactivity, the proportion of chemical B needs to be increased. What quantity (in gm) of chemical B should be added to the remaining mixture in order to make the concentration of chemical B in it as 60%?
75
60
50
80
Q4. A vessel contains 20 litres of pure milk. A person takes out 2 litres of milk from the vessel and replaces it with 2 litres of water. Again, 2 litres of the mixture is taken out and replaced with 2 litres of water. If this process is repeated one more time but the mixture taken out is replaced with 2 litres of milk, then what is the quantity (in litres) of milk left in the mixture?
14.68
16.58
15.48
17.28
Q5. Liquids A and B are combined in a container in the ratio 11:13. After removing some of the mixture and adding some liquid C, the ratio of the liquids A, B, and C changed to 22: 26: 23. The amount of mixture in the container was 10 litres less overall after adding liquid C than it was before. Find the original volume (in litres) of liquid B in the container if the volume of liquid A removed from the container is 120 litres less than the volume of liquid C added to the container.
360
350
390
330
Q6. A vessel is filled to its capacity with pure milk. Eight liters are withdrawn from the vessel and replaced with an equal amount of water. Eight liters of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes, the vessel contains 15.2 liters of milk less than it did initially. What is the minimum number of such additional replacements required, so that the vessel contains less than 55% milk?
2
5
4
3
Q7. 100 ml of liquid A is mixed with ‘y’ ml of liquid B. Then, 40 ml of this A-B mixture is added to 2y ml of another A-B mixture with liquid A concentration of 26%. If the resultant mixture has a liquid B concentration of 2y%, what is the value of ‘y’ in milliliters?
Q8. A tetra pack contains 1 litre of milk and a vessel contains 2 litres of water. Initially, 0.5 litres of milk is transferred from the tetra pack to the vessel. After stirring this mixture, 0.5 litres of this mixture is transferred from the vessel to the tetra pack. At this point, the quantity of water in the tetra pack is x while that of the milk in the vessel is y, then the ratio x: y must be:
1: 2
2: 1
3: 2
1: 1
Q9. Three solutions have acid content 30%, 40% and 80% respectively. A mixture has been made with these three solutions where the volume of these solutions used are x ml, y ml, and z ml respectively. Which of the following will be true about the maximum value of the resulting concentration if z = 2x < y?
less than 54
54 or more but less than 55
55 or more but less than 56
56 or more
Q10. A new stock of shirts has arrived at Vinit’s shop. The shirts are packed in two boxes. In the first box, out of 90 shirts, 30% are red. If 70% of the shirts in the second box are red, the overall percentage of red shirts would be 40%. If the percentage of red shirts in the second box had been 90% (instead of 70%), the overall percentage of red shirts would have been:
45%
50%
60%
70%
Q11. A pitcher is filled with corn syrup and a second pitcher is filled with pure water. Half of the corn syrup and half of the pure water is poured into a large glass bowl. Next, one-third of the remaining corn syrup from the first pitcher and half of the remaining pure water from the second pitcher is again poured into the glass bowl. Now, the volumes of corn syrup and pure water left in the two pitchers are the same. Then the ratio of corn syrup and pure water in the large glass bowl is:
1: 1
3: 2
2: 3
8: 3
Q12. There are two milk containers, each containing a solution of milk and water. In the first container, milk and water are in the ratio 5: 3. Solutions from the first container and second container are mixed in the ratio 2: 5. Milk and Water are in the ratio 17: 11 in the resultant mixture. In the second container, the ratio of milk to water is:
3: 2
2: 3
3: 5
5: 3
Q13. Container-A is fully filled with one litre pure milk. Milkman Harman poured one-third of the content of container-A by volume to a large empty bowl. Then he refills container-A till its brim with pure water without any wastage and again empties half the mixture of container-A to that large bowl. At last, he fills container-A till its brim with pure water without any wastage and completely empties its content in the large bowl. What is the concentration (in %) of milk in the solution contained in the large bowl now?
Q14. Three different alloys, of copper and iron, have the two elements in the ratio 3: 5, 3: 7 and 12: 5 respectively. If 8 kg of the first alloy and 30 kg of the second alloy are taken, then how much quantity (in kg) of the third alloy should be taken so that the ratio of copper and iron in the final mixture is 1: 1?
51
34
68
17
Q15. If a milkman mixes 30 litres of pure milk with 10 litres of milk-water solution, the concentration of water in the resulting solution becomes 12.5%. If the milkman had sold only the 10 litres milk-water solution at the cost price of pure milk without any wastage, his profit percentage would have been:
Q16. A milkman doubled the volume of pure milk by adding water. He further adds pure milk to the resultant solution to increase its volume by 25%. What is the concentration of milk (in percentage) in this final solution?
Q17. A milk-water mixture of volume 200 litres contains 10% water. How many litres of water must be added to the mixture so that the percentage of water increases to 40%?
Q18. How many kilograms of rice costing Rs.60 per kg must be mixed with 15 kg of rice costing Rs.80 per kg so that the resulting mixture costs Rs.72 per kg?
Q19. Vessels X and Y contain mixtures of milk and water. X has x% milk and Y has y% milk. Mixture R is formed by mixing x% of vessel X’s contents with (100 – y)% of vessel Y’s contents. Mixture S is formed by mixing (100 – x)% of vessel X’s contents with y% of vessel Y’s contents. Mixtures R and S have k% milk each. If x ≠ y and all measures are in ml, find x + y.
75 ml
80 ml
90 ml
100 ml
Q20. Jar A and Jar B have 6 litres of milk and 6 litres of water respectively. A jar C with volume of ‘v’ litres is filled with the milk from Jar A and then emptied into B. Jar C is then filled with the mixture so formed, and then emptied into Jar A. If the ratio of milk to water in Jar A at this stage is 3: 1, find the value of ‘v’.
Q21. There are two vessels of mixture A of different prices with the volumes of 240 liters and 160 liters. Equal amounts of A were poured off simultaneously from the two vessels. Now, that mixture A poured off from the first vessel was poured into the second vessel, and similarly the mixture A poured off from the second vessel was poured into the first vessel. Then the price of mixture A in both vessels becomes the same. How much mixture A (in liters) was poured from one vessel into the other?
Q22. There are three vessels V1, V2, and V3 with equal volumes filled with mixtures of liquids A and B in the ratios 1: 2, 2: 3, and 2: 7, respectively. These mixtures are boiled (assume that only B evaporates) till the concentration of A in the three vessels becomes 40%, 60%, and 50% respectively. Then they are all poured into a big vessel. Find the ratio of liquids A: B in the big vessel.
43:44
47:53
86:87
86:89
Q23. There are three vessels (with equal volumes) filled with mixtures of water and milk in the ratios 1: 2, 4: 5, and 5: 4, respectively. These mixtures are then poured into a larger vessel. What proportion of the mixture in the larger vessel should be replaced with water to ensure that the resulting mixture contains 50% milk?
1/10th
1/5th
1/8th
1/12th
Q24. There is an alloy ‘A’ of silver and copper. A certain weight of this alloy is mixed with 20 kg of pure silver and melted; the new alloy ‘B’ is found to contain 80% of silver. If the alloy ‘A’ is mixed with 15 kg of 80% silver alloy, the new alloy ‘C’ is found to contain 75% silver. What is the ratio of the weights of silver and copper in alloy ‘A’?
48:17
3:1
11:4
49:18
Q25. From a 4: 5, solution of milk and water, a volume equal to 25% is taken out and replaced by milk. How many times should this process be done to make the ratio of milk to water equal to 11: 5?
1
2
3
4
Q26. A scientist has a conical flask that has 400 ml of a mixture of liquids A and B in the ratio 7: 1 respectively. Each time the flask is heated A and B evaporate in the ratio 4: 1. As soon as the volume dips to 90% of the original volume the scientist adds more of B to make it 400 ml again. How many times does he add liquid B in this way to make the concentration of A in the mixture less than 50%?
3
4
5
6
Q27. A vessel V1 contains a mixture of milk and water in a ratio of 7: 3. If 20 liters of this mixture is taken out and poured into vessel V2 that already contains milk and water in the ratio 4: 1, then the difference between total quantity of milk and water in V2 becomes 50 liters. Find the total quantity (in liters) of initial mixture in vessel V2.
Q28. A jar contains 2 liquids A and B. A is a volatile liquid and evaporates at the rate of 4 liters per minute. Liquid B is stable. At the end of the 8th minute if the ratio of volumes of A and B is 4: 9, then what is the original volume (in liters) of this mixture given that the original ratio of the volumes is 4: 5?
Q29. An immiscible mixture contains three different types of liquids A, B and C. The ratio of liquids A and B is 1: 2 and the volume of liquid C is 20 litres. 5 litres of C and 2 litres of A are replaced by equal volumes of liquid B. The ratio of liquids A and B becomes 1: 3. Find the volume of the mixture (in litres).
63
61
59
65
Q30. A mixture of liquids A and B contains 70% of B by volume. Liquid C is added till the final solution contains 12% by volume of A. What is the ratio (by volume) of B to C in the final mixture?
7: 15
3: 11
7: 25
1: 5
Q31. One litre of liquid A weighs 2 kg, while one litre of liquid B weighs 1.5 kg. If the 800 ml of the mixture of liquid A and liquid B weighs 1.5 kg, what is the ratio of liquid A and liquid B in the mixture by volume?
3: 2
3: 1
1: 3
2: 3
