CAT Mixtures and Alligation questions with solutions
Mixing, replacement and alligation problems. 35 questions from our 2016–2025 CAT pattern papers. Each has the answer and a full solution.
CAT 2025
- How many litres of water must be added so that the ratio of milk to water becomes 3:1?
- A shopkeeper mixes milk solution A (milk:water = 5:1) with milk solution B (milk:water = 2:1) to obtain a mixture in which milk:water = 3:1. In what…
- Alloy A has copper and zinc in the ratio 3:2, while alloy B has copper and zinc in the ratio 1:3. In what ratio should A and B be mixed so that the…
- 20 litres of the mixture is withdrawn and replaced with water; this operation is repeated once more (a total of two withdraw-and-replace operations).…
CAT 2024
- Alloy A contains copper and zinc in the ratio 3:2, and alloy B contains them in the ratio 1:3. If equal quantities (by weight) of A and B are melted…
- How many litres of water must be added to change the ratio of milk to water to 5:6?
- A container holds 54 litres of a mixture of acid and water in the ratio 7:2. How many litres of water must be added so that the new ratio of acid to…
- A shopkeeper mixes two varieties of rice costing ₹60/kg and ₹90/kg. He sells the mixture at ₹96/kg, making a 20% profit. If the cheaper variety is…
- 8 litres of this mixture is removed and replaced with pure water. What is the new ratio of milk to water?
CAT 2023
- Alloy A has copper and zinc in the ratio 3:2, and alloy B has copper and zinc in the ratio 1:3. Equal weights of A and B are melted together. Find…
- 20 litres of milk is drawn off and replaced with water; the vessel is mixed well. Then 20 litres of this mixture is drawn off and again replaced with…
- A container has 81 litres of pure milk. 27 litres is drawn off and replaced with water; this process is repeated once more (i.e., done twice in…
CAT 2022
- How many litres of water must be added to make the ratio of milk to water 5:4?
- Three varieties of tea costing ₹120/kg, ₹150/kg and ₹200/kg are mixed in the ratio 2 : 3 : 5 by weight. Find the cost per kg of the resulting mixture.
- 8 litres of milk is withdrawn and replaced with water; the same process (withdraw 8 litres of the mixture, replace with water) is repeated once more.…
- A vessel contains a mixture of milk and water in the ratio 5 : 3. 32 litres of this mixture is drawn off and replaced with water, after which the…
CAT 2021
- Twenty litres of the mixture are drawn off and replaced with water. How many litres of pure milk must now be added so that the ratio of milk to water…
- 16 litres are drawn out and replaced by water. This operation is carried out three times in all.
- In what ratio must a grocer mix rice costing ₹60 per kg with rice costing ₹80 per kg so that, after selling the mixture at ₹84 per kg, he makes a…
CAT 2020
- Vessel A contains milk and water in the ratio 5 : 3 and vessel B contains milk and water in the ratio 2 : 3. In what ratio should the contents of A…
- A certain quantity x litres is removed and replaced with water. This operation is performed once more with the same x. The container now has milk and…
- Alloy X contains copper and zinc in the ratio 3 : 2, and alloy Y contains them in the ratio 2 : 1. In what ratio (by weight) must X and Y be mixed so…
- A vessel contains 80 litres of pure milk. 16 litres are drawn out and replaced with water. This operation is performed three times in all. How many…
- This operation is performed two more times (three operations in all). How many litres of milk remain in the container at the end?
- Alloy P contains copper and zinc in the ratio 3 : 2, and alloy Q contains them in the ratio 5 : 3. In what ratio should P and Q be mixed (by weight)…
CAT 2019
- A cistern is filled with 80 litres of pure milk to begin with. On four separate occasions, 8 litres of the mixture currently in the cistern are drawn…
- Sixteen litres of the mixture are removed and replaced with water. This operation (remove 16 litres of the mixture, replace with 16 litres of water)…
- Alloy X contains gold and copper in the ratio 5 : 3, and alloy Y contains them in the ratio 7 : 5. How many kilograms of alloy X must be melted with…
CAT 2018
- How many litres of water must be added to make the ratio of milk to water 3 : 2?
- A container is full with 80 litres of pure milk. This operation is performed a total of three times. How many litres of milk are left in the…
- This operation is done three times in all. How many litres of milk remain in the vessel?
CAT 2017
CAT 2016
Other Quant topics
Time, Speed and Distance 38Time and Work 23Pipes and Cisterns 11Simple and Compound Interest 33Profit, Loss and Discount 42Ratio and Partnership 17Percentages 30Averages 19Permutations, Combinations and Sets 28Probability 20Logarithms and Indices 16Quadratic Equations and Polynomials 18Linear Equations 9Inequalities and Modulus 19Functions 22Maxima and Minima 11Progressions 29Remainders and Divisibility 15Number System 19Coordinate Geometry 29Triangles 24Circles 18Polygons and Quadrilaterals 12Mensuration 13