SSC CGL 2027 Mixture and Alligation Questions for Tier 1

Mixture and alligation is a useful arithmetic topic for SSC CGL Quantitative Aptitude preparation. Questions commonly involve mixing two products with different prices or concentrations, finding the ratio in which they should be mixed, and calculating the average price or concentration of the resulting mixture.

Understanding the alligation method can help candidates solve these questions without lengthy calculations. In this guide, you will learn the basic concepts, important formulas, solved examples, shortcuts, and practice questions with answers for SSC CGL 2027 Tier 1 preparation.

1. What Is a Mixture?

A mixture is formed when two or more substances are combined. The substances may have different prices, concentrations, or proportions. In competitive-exam questions, you may need to calculate the average cost, final concentration, or ratio of the quantities mixed.

For example, if rice costing ₹40 per kg is mixed with rice costing ₹60 per kg, the average cost depends on the quantities of each type used.

Remember: The average value of a mixture must lie between the values being mixed when both quantities are positive.

2. What Is the Alligation Method?

Alligation is a shortcut used to find the ratio in which two ingredients with different values must be mixed to obtain a desired average value.

Example: In what ratio should rice costing ₹40 per kg and ₹60 per kg be mixed to obtain a mixture worth ₹48 per kg?

Cheaper price = ₹40 per kg.

Dearer price = ₹60 per kg.

Mean price = ₹48 per kg.

Cheaper : Dearer = (60 − 48) : (48 − 40)

= 12 : 8

= 3 : 2

Answer: Mix the cheaper and dearer rice in the ratio 3:2.

3. Solved Questions on Average Price

Example 1: Mixing Two Types of Rice

Question: Rice costing ₹30 per kg is mixed with rice costing ₹50 per kg to obtain a mixture worth ₹38 per kg. Find the ratio of cheaper rice to dearer rice.

Solution:

Cheaper : Dearer = (50 − 38) : (38 − 30)

= 12 : 8

= 3 : 2

Answer: 3:2.

Example 2: Finding the Mean Price

Question: Five kilograms of tea costing ₹200 per kg are mixed with three kilograms of tea costing ₹280 per kg. Find the average cost per kg.

Solution:

Total cost of first tea = 5 × ₹200 = ₹1,000.

Total cost of second tea = 3 × ₹280 = ₹840.

Total cost = ₹1,840.

Total quantity = 5 + 3 = 8 kg.

Average cost = ₹1,840 ÷ 8 = ₹230 per kg.

Answer: ₹230 per kg.

4. Milk and Water Mixture Questions

Milk and water questions often involve finding the ratio of milk to water, calculating the amount of water added, or determining the final concentration of milk in a mixture.

When water is added to pure milk, the quantity of milk remains unchanged while the total volume increases. This distinction is important when calculating the final proportion.

Example 3: Finding the Quantity of Water

Question: A container contains 24 litres of milk. How much water must be added to make the ratio of milk to water 4:1?

Solution:

Milk : Water = 4 : 1.

Four parts represent 24 litres of milk.

One part = 24 ÷ 4 = 6 litres.

Water required = 6 litres.

Answer: 6 litres of water.

Example 4: Finding Milk Concentration

Question: A mixture contains 30 litres of milk and 10 litres of water. What percentage of the mixture is milk?

Solution:

Total mixture = 30 + 10 = 40 litres.

Milk percentage = (30 ÷ 40) × 100 = 75%.

Answer: 75%.

5. Replacement Method in Mixture Questions

Some questions involve removing part of a mixture and replacing it with another liquid. When a quantity is removed from a well-mixed solution, the removed liquid contains the same proportions of the original ingredients as the mixture itself.

If a container holds V litres of a well-mixed liquid and x litres are removed and replaced with water, the fraction of the original liquid remaining after one replacement is:

For repeated removal and replacement with water, the quantity of the original liquid remaining after n operations is:

V × (1 − x/V)ⁿ

This formula assumes the container is mixed thoroughly before each removal and the same quantity is removed and replaced each time.

Example 5: One Replacement

Question: A container has 40 litres of pure milk. Ten litres are removed and replaced with water. How much milk remains?

Solution:

Milk removed = 10 litres.

Milk remaining = 40 − 10 = 30 litres.

Water added = 10 litres.

Total mixture = 40 litres.

Answer: 30 litres of milk remain.

6. Important Shortcuts and Exam Tips

• Use alligation for two values: It is often faster than forming equations when two prices or concentrations are given.
• Check the mean: The desired average must lie between the two values for a positive mixture of both ingredients.
• Use weighted average: When quantities are given, multiply each value by its quantity and divide the total by the combined quantity.
• Track units: Keep kilograms, litres and prices per unit consistent.
• Separate quantity from concentration: Adding water increases total volume but does not increase the quantity of milk.
• Verify the ratio: Check whether the calculated quantities produce the required average.

7. Common Mistakes to Avoid

1. Reversing the terms in the alligation ratio.
2. Using the simple average of two prices when the quantities are unequal.
3. Forgetting to calculate the total quantity after adding water.
4. Assuming that removing a mixture removes only one ingredient.
5. Using the repeated-replacement formula without assuming thorough mixing.

8. Practice Questions for SSC CGL 2027

Try these questions before checking the answer key.

Answer Key with Explanations

1. B) 3:2: Cheaper : Dearer = (35 − 26) : (26 − 20) = 9:6 = 3:2.

2. C) ₹46: Total cost = (4 × 40) + (6 × 50) = ₹460. Total quantity = 10 kg. Average = ₹460 ÷ 10 = ₹46 per kg.

3. D) 75%: Total mixture = 18 + 6 = 24 litres. Milk percentage = 18/24 × 100 = 75%.

4. C) 15 litres: The removed liquid is pure milk, so 20 − 5 = 15 litres of milk remain.

5. B) 2:1: Using alligation, the ratio of the first liquid to the second is (50 − 30):(30 − 20) = 20:10 = 2:1.

9. How to Prepare Mixture and Alligation

Begin by practising weighted averages and simple ratio calculations. Next, learn the alligation shortcut and apply it to price and concentration problems. Once these basics are clear, practise milk-and-water and replacement questions.

Maintain a formula notebook and solve a small set of questions under timed conditions. After each session, review errors in ratio order, arithmetic and units. Understanding why a shortcut works is more useful than memorising it without context.

Check the official SSC CGL notification and syllabus when released for the applicable 2027 examination details. This article is a preparation resource and does not guarantee that a particular question will appear in the examination.

Frequently Asked Questions

1. What is the alligation method?

Alligation is a shortcut for finding the ratio in which two values should be mixed to obtain a desired mean.

2. When should I use weighted average instead of alligation?

Use weighted average when the quantities of the ingredients are given. Alligation is especially useful when you need to find their mixing ratio.

3. How do you solve milk-and-water questions?

Calculate the total volume and identify the quantity of milk and water separately. Apply the changes described in the question carefully.

4. Can alligation be used for concentration questions?

Yes. It can be used when mixing two concentrations to obtain a target concentration between them.

5. How can I improve my speed in mixture questions?

Practise alligation, weighted averages and ratio simplification, then review your calculation errors regularly.