Mixture and Alligation Questions for CLAT 2027: Download PDF

What is a Mixture?

A mixture is made up of the combination of two or more quantities or substances.

For instance, if 5 litres of milk are mixed with 3 litres of water, the mixture made will have:

• Milk = 5 litres

• Water = 3 litres

• Mixture = 8 litres

Mixture problems may be in terms of quantities, cost, percentage, concentration and many others.

A typical mixture problem is one in which the candidates are required to calculate the proportion in which the two substances must be mixed to get a certain average cost or concentration.

What is Alligation?

Alligation is the mathematical approach that helps to find the proportion in which two items of different values must be mixed so as to get a mixture of a particular value.

In the case of two items with values A and B being mixed to give a mean value M,

the proportion of their quantities will be:

• Quantity of cheaper item/ lower value item: Quantity of costlier item/ higher value item = (B − M) : (M − A)

For example, in the case of mixing rice priced at Rs 40/kg with rice priced at Rs 60/kg to give a mixture of value Rs 50/kg,

• Proportion = (60 − 50) : (50 − 40)

• = 10:10

• = 1:1

Important Mixture and Alligation Formulas for CLAT 2027

Candidates must keep the following formulas in mind:

• Average value of mixture = Total value / Total quantity

For price questions:

• Average Price = Total Cost / Total Quantity

For concentration:

• Concentration = Quantity of substance / Total quantity * 100

The formula for alligation is:

• Lower value: Higher value = (Higher value – Mean value) : (Mean value – Lower value)

Candidates must be cautious regarding the sequence of values while applying the formula.

Types of Mixture and Alligation Questions

1. Simple Questions on Mixtures

This involves questions where two or more quantities are mixed together.

For instance, if 4 litres of one substance is mixed with 6 litres of another substance, then the amount of mixture formed will be:

• 4 + 6 = 10 litres

From here, the question may ask about the amount of one substance in the resultant mixture.

2. Questions based on Price of Mixtures

These questions involve two substances that have different prices.

For instance, suppose we mix tea that costs Rs 100 per kg and other tea that costs Rs 140 per kg. The question may ask what ratio we use to get a mixture at Rs 120 per kg.

With the help of alligation,

• Ratio = (140 – 120):(120 – 100)

• = 20:20

• = 1:1

3. Mixture Based on Concentration

This involves the use of solutions of different concentrations.

For instance, a 20% solution and a 50% solution can be combined to get a 30% solution.

• Ratio = (50 - 30):(30 - 20)

• = 20:10

• = 2:1

Hence, 20% and 50% solutions should be combined in the ratio of 2:1.

4. Replacement Questions

In some questions, part of the mixture is removed and replaced by some other material, usually water.

The questions may be a little difficult as the concentration changes with each removal. It is important for candidates to calculate the amount left after each process.

5. Mixture and Ratio Questions

There may be some questions that give the ratio of the two substances and ask the candidates to find out the amount of one substance or the total mixture.

These questions require candidates to combine the knowledge of ratio and mixture.

How to Solve Mixture and Alligation Questions Faster

Step one is to ascertain what the question is looking for. Identify whether the question entails price, concentration, quantity, ratio or replacement.

In simple two-valued mixture problems, the alligation rule saves a lot of time. The candidates need to understand the reason behind the rule rather than simply memorising it.

For instance, in cases where two prices are mixed to give a middle price, the quantity of the cheaper good should be more if the price you want to achieve is nearer to the cheaper good. In the same vein, the quantity of the costlier good will be more if the price you want to get is nearer to the costlier good.

Candidates need to make sure that the units are the same before solving any question.

Common Mistakes to Avoid

The errors that candidates commonly make in the case of mixture problems are as follows:

• Using the alligation method in the wrong order.

• Mixing up the ratio of quantities with that of prices.

• Failing to change units.

• Confusing the percentage of concentration with that of quantity.

• Using the arithmetic mean where the weighted average should be used.

• Neglecting the quantity of each item.

• Mistakes made in replacement problems.

• Rounding off numbers too soon.

One very important thing to remember is that the average price of a mixture will not exceed the highest price, nor can it be below the lowest price of the items included in the mixture.

CLAT 2027 Preparation Strategy for Mixture and Alligation Questions

Candidates need to start by revising ratios, proportions, percentages, and averages, which are common in mixture problems.

Start with easy problems based on two quantities and then proceed to problems based on prices and concentration; after solving all these, practice problems related to replacements and multiple steps.

Solve CLAT Quantitative Techniques practice questions regularly within time limits. This will make the candidate comfortable with calculations and time management.

Candidates can have a list of formulas in short notes for revisions; however, they must try solving problems without seeing formulas. This will help them become familiar with concepts.

After attempting every set of practice questions, analyse wrong answers and know the exact reason for mistakes. This is more helpful in mixture problems because most mistakes are made in the ratio part, not the calculation part.

Mixture and Alligation Practice Questions for CLAT 2027

Q1. Rice costing Rs 30 per kg is mixed with rice costing Rs 50 per kg to obtain a mixture costing Rs 40 per kg. In what ratio should the two varieties be mixed?

A) 1:2
B) 2:1
C) 1:1
D) 3:2

Answer: C) 1:1

Q2. A 20% solution is mixed with a 50% solution to obtain a 30% solution. What should be the ratio of the 20% solution to the 50% solution?

A) 1:2
B) 2:1
C) 3:2
D) 2:3

Answer: B) 2:1

Q3. A mixture contains 30 litres of milk and 10 litres of water. What is the ratio of milk to water?

A) 2:1
B) 3:1
C) 1:3
D) 4:3

Answer: B) 3:1