300+ Most Important Arithmetic Questions for CAT
Alligation Mixture
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Arithmetic
- Average
- Ratio and Partnership
- Percentage
- Simple Interest & Compound Interest
- Profit & Loss
- Time and Work
- Alligation Mixture
- Time, Speed & Distance
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?
