CAT Mixtures & Alligation Questions

Mixture problems combine quantities with different concentrations, prices or other values. Alligation is a shortcut for a two-component weighted average; replacement problems require tracking what remains.

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Key concepts

Weighted average
Alligation ratios
Concentration and repeated replacement

CAT mixtures & alligation practice questions

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Practise Free Tests on InsideIIM

Common mistakes

Reversing the alligation ratio.
Applying a fixed replacement formula when the amount removed varies.

Practical solving approaches

Write a balance equation for the substance or value being mixed.
Use alligation only when the target lies between the component values, and handle unequal replacements step by step.

Mixtures & Alligation FAQs

Can alligation be used for more than two ingredients?: A balance equation works for multiple ingredients. The basic cross-difference shortcut gives the ratio for two components, so extra conditions are needed for larger mixtures.

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CAT mixtures & alligation practice questions

Question 1Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

John sells cornflour at the rate of Rs.5.10 per kg and gains a profit of 20%. If he decreases the price so as to gain only 25 p. per kg, what should be the ratio in which the sales should increase so as to get the same amount of profit?

Question 2Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Question 3Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows :

From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

Question 4Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

There are two beakers I and II filled with 100 ml of alcohol and 100 ml of water respectively. First, 10 ml of water is poured from beaker II to beaker I. Then, 11 ml mixture from beaker I is poured back into beaker II. Then from this new mixture in beaker II, 1 ml is poured back into beaker I. Which of the following statements is true?

Question 5Multiple choiceMEDIUM

Select the correct alternative from the given choices.

1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

Question 6Multiple choiceMEDIUM

Select the correct alternative from the given choices.

100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

 

Question 7Multiple choiceEASY

Select the correct alternative from the given choices.

3L of milk is drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

Question 8Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?

Question 9Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A milkman purchases milk at Rs 20/litre and mixes 4 litres of water in it. By selling the resultant mixture at the rate of Rs 20/litre, he earns a profit of 40%. The amount of mixture he had with him to sell was:

Question 10Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A man buys juice at Rs 10/litre and dilutes it with water. He sells the mixtures at the cost price and thus gains 11.11%. Find the quantity of water mixed by him in every litre of juice.

Question 11Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Two tanks of similar volume are full of a mixture of oil and water. In the first, the ratio of oil and water is 5:8 and in the second, it is 7:19. If both these tanks are poured in a larger tank, what would be the resultant ratio of oil and water?

Question 12Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A vessel is full of a mixture of methanol and ethanol in which there is 20% ethanol. 10 litres of mixture are drawn off and filled with methanol. If the ethanol is now 15%, what is the capacity of the vessel?

 

Question 13Multiple choiceMEDIUM

Select the correct alternative from the given choices.

What would be the ratio of milk and water in a final mixture formed by mixing milk and water that are present in three vessels of capacity 1l, 2l, and 3l respectively and in the ratios 5:1, 3:2 and 4:3 respectively?

Question 14Multiple choiceMEDIUM

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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).

Question 15Multiple choiceMEDIUM

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A mixture of liquids P, Q and R, contains the three in the ratio 2 : 4 : 7 respectively. P and Q are added till the ratio
becomes 7 : 4 : 2. Find the ratio of the amounts of P and Q added.

Question 16Multiple choiceMEDIUM

Select the correct alternative from the given choices

A grain merchant purchases two variees of rice; the price of the first kind being twice that of the second. He
mixes the two variees and sells for Rs.28 per kg making a profit of 25%. If the rao of the quanty of the first to
the second kind of rice is 2 : 3 in the mixture, then the cost of costlier variety is:

Question 17Multiple choiceMEDIUM

Select the correct alternative from the given choices

A certain quantity of a mixture of oil and water in the ratio 5: 8, (called mixture A) is mixed with an equal volume of another mixture
of oil and water (called mixture B), such that the ratio of oil and water in the resultant mixture is 7: 6. What is the ratio of oil and
water in the mixture B?

CAT mixtures & alligation practice questions

Question 1Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Question 2Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Question 3Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows :

Question 4Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Question 5Multiple choiceMEDIUM

Select the correct alternative from the given choices.

1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

Question 6Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 7Multiple choiceEASY

Select the correct alternative from the given choices.

3L of milk is drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

Question 8Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?

Question 9Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 10Multiple choiceMEDIUM

Select the correct alternative from the given choices.

A man buys juice at Rs 10/litre and dilutes it with water. He sells the mixtures at the cost price and thus gains 11.11%. Find the quantity of water mixed by him in every litre of juice.

Question 11Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 12Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 13Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 14Multiple choiceMEDIUM

Select the correct alternative from the given choices

Question 15Multiple choiceMEDIUM

Select the correct alternative from the given choices

A mixture of liquids P, Q and R, contains the three in the ratio 2 : 4 : 7 respectively. P and Q are added till the ratio
becomes 7 : 4 : 2. Find the ratio of the amounts of P and Q added.

Question 16Multiple choiceMEDIUM

Select the correct alternative from the given choices

Question 17Multiple choiceMEDIUM

Select the correct alternative from the given choices

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CAT Mixtures & Alligation Questions

Key concepts

CAT mixtures & alligation practice questions

Common mistakes

Practical solving approaches

Mixtures & Alligation FAQs

CAT Mixtures & Alligation Questions

Key concepts

CAT mixtures & alligation practice questions

Common mistakes

Practical solving approaches

Mixtures & Alligation FAQs

More Arithmetic practice

CAT Mixtures & Alligation Questions

Key concepts

CAT mixtures & alligation practice questions

Common mistakes

Practical solving approaches

Mixtures & Alligation FAQs

CAT Mixtures & Alligation Questions

Key concepts

CAT mixtures & alligation practice questions

Common mistakes

Practical solving approaches

Mixtures & Alligation FAQs

More Arithmetic practice