Mixture and Alligation Questions for SSC Exam Preparation

When you use long algebraic approaches to tackle mixture and alligation problems, they generally take too long.

This can make you slower and less accurate on tests like SSC CGL and CHSL. That's why it's crucial to know how to answer mixture and alligation questions for SSC.

They help you tackle these kinds of problems fast and easily. This article makes the ideas clear and useful, so you can use them well in the quantitative aptitude section.

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What Are the Basics of Mixture and Alligation?

A mixture is the result of combining two or more ingredients in a specific ratio.

Alligation, on the other hand, is a mathematical rule or a "shortcut" that helps us determine the ratio in which two ingredients at different prices must be mixed to produce a mixture at a desired price.

For students preparing for SSC CGL, the "Rule of Alligation" is the most vital tool. It allows you to find the proportion between a cheaper quantity and a dearer quantity.

The Alligation Rule 

To use this method, you need three values:

• Cheaper Price (C): The lower cost price of one ingredient.

• Dearer Price (D): The higher cost price of the second ingredient.

• Mean Price (M): The cost price of the final mixture.

The ratio of the quantities is calculated as:

(Quantity of Cheaper) / (Quantity of Dearer) = (Dearer Price - Mean Price) / (Mean Price - Cheaper Price)

Check Out: SSC Previous year Papers

Mixture and Alligation Questions for SSC

To really do well, you need to understand how these rules work in situations. Here are some mixture and allegation questions for SSC CGL and CHSL, with step-by-step explanations that will help you learn the topic. 

Question 1: Finding the Mixing Ratio

Problem: In what ratio must a grocer mix tea at 150 per kg and 200 per kg so that the mixture is worth 165 per kg?

Detailed Solution:

• Step 1: Identify the components. Cheaper price (C) = 150; Dearer price (D) = 200; mean price (M) = 165.

• Step 2: Subtract the mean price from the dearer price: 200 - 165 = 35.

• Step 3: Subtract the cheaper price from the mean price: 165 - 150 = 15.

• Step 4: The ratio of cheaper to dearer is 35:15.

• Step 5: Simplify the ratio by dividing by 5. The result is 7 :3.

Question 2: The Profit and Loss Twist

Problem: In what ratio must rice at 62 per kg be mixed with rice at 72 per kg so that by selling the mixture at 75.90 per kg, the shopkeeper gains 15%?

Detailed Solution:

• Step 1: Note that 75.90 is the Selling Price (SP). Alligation requires the cost price (CP).

• Step 2: Calculate CP of the mixture: CP = (SP / (100 + Profit %)) * 100 = (75.90 / 115) * 100 = 66 per kg.

• Step 3: Use Alligation with 62, 72, and 66.

• Step 4: (72 - 66) = 6 and (66 - 62) = 4.

• Step 5: Ratio = 6:4, which simplifies to 3:2.

Question 3: Adding a Pure Component (Water)

Problem: A 40-litre mixture of milk and water contains 10% water. How much water must be added to achieve a 20% water content in the new mixture?

Detailed Solution:

• Step 1: Focus on water. Initial water = 10%. Added water = 100% (since it is pure).

• Step 2: Target mean concentration = 20%.

• Step 3: Apply Alligation: (100 - 20) = 80; (20 - 10) = 10.

• Step 4: The ratio of the original mixture to added water is 80:10 or 8:1.

• Step 5: If 8 parts equal 40 litres, then 1 part equals 5 litres.

Question 4: Two Mixtures Combined

Problem: Two vessels, A and B, contain milk and water in ratios 5:2 and 8:5, respectively. In what ratio should these be mixed to get a new mixture containing milk and water in the ratio 9:4?

Detailed Solution:

• Step 1: Focus on one component, say, milk.

• Step 2: Milk in A = 5/7; Milk in B = 8/13; Target Milk = 9/13.

• Step 3: Apply Alligation: (9/13 - 8/13) = 1/13; (5/7 - 9/13) = (65 - 63) / 91 = 2/91.

• Step 4: Ratio = 1/13:2/91. Multiply by 91 to clear denominators.

• Step 5: Result = 7:2.

Question 5: Successive Replacement

Problem: A container contains 80 litres of milk. In this container, 8 litres of milk were taken out and replaced with water. This process was repeated twice more. How much milk is in the container now?

Detailed Solution:

• Step 1: Initial quantity (x) = 80; amount replaced (y) = 8; total operations (n) = 3.

• Step 2: Formula: Final = Initial * [1 - (y/x)] to the power of n.

• Step 3: Final Milk = 80 * [1 - (8/80)] to the power of 3.

• Step 4: Final Milk = 80 * (9/10) * (9/10) * (9/10) = 80 * (729 / 1000).

• Step 5: Result = 58.32 litres.

Question 6: Mixing Two Varieties of Sugar
A shopkeeper mixes sugar worth ₹40 per kg with sugar worth ₹55 per kg. In what ratio should both be mixed so that the final mixture costs ₹46 per kg?

Solution:
Here, cheaper price = ₹40, dearer price = ₹55, and mean price = ₹46.
Using alligation:
Dearer price - Mean price = 55 - 46 = 9
Mean price - Cheaper price = 46 - 40 = 6
So, the ratio of cheaper sugar to dearer sugar is 9:6, which becomes 3:2.

Question 7: Milk and Water Mixture
A 60-litre mixture contains milk and water in the ratio 4:1. How much water should be added to make the ratio 3:1?

Solution:
In 60 litres, milk = 48 litres and water = 12 litres. Since only water is added, milk remains 48 litres.
For the new ratio to be 3:1, if milk is 48 litres, water should be 16 litres.
Current water = 12 litres. So, water to be added = 16 - 12 = 4 litres.

Question 8: Selling Price with Profit
A trader mixes two types of rice costing ₹50 per kg and ₹70 per kg. He sells the mixture at ₹72 per kg and earns 20% profit. In what ratio should the rice be mixed?

Solution:
First, find the cost price of the mixture.
CP = 72 × 100 / 120 = ₹60 per kg.
Now apply alligation with ₹50, ₹70, and ₹60.
70 - 60 = 10 and 60 - 50 = 10.
So, the required ratio is 1:1.

Question 9: Replacement-Based Question
A vessel has 50 litres of pure milk. 10 litres are removed and replaced with water. How much milk is left?

Solution:
Milk removed = 10 litres, so milk left = 40 litres.
After adding 10 litres of water, the total mixture is again 50 litres.
So, the vessel now contains 40 litres of milk and 10 litres of water.

Practise these mixture and alligation for SSC CGL to perform better. 

Check Out: SSC Mathematics Chapterwise & Topicwise PYQs

Importance of Mixture and Alligation Questions for SSC

In the CGL Tier 1 and CGL Tier 2 exams, time management is the difference between selection and rejection. Traditional equations can be very long and complicated. 

The CGL Tier 1 and 2 mixture and alligation questions for SSC CHS often have a lot in common with topics such as profit and loss, simple interest, and average for SSC CGL exams.

Using the alligation cross-diagram helps you:

1. Reduce Calculation Time: Avoid long divisions and complex variables.

2. Visualise the Problem: The cross method provides a clear path to the answer.

3. Apply to Multiple Topics: You can use this to find average speeds or interest rates for two different investments.

Read More: SSC Maths Syllabus and Important Topics

Mixture and Alligation Questions for SSC FAQs

What is the main difference between mixture and alligation?

A mixture is when you combine two or more things together. Alligation is a way to figure out how much of each to mix together based on their costs. Alligation helps you find the ratio of a mixture.

Can I use alligation for profit and loss questions?

You can definitely use mixture and alligation questions to learn SSC techniques for solving profit-and-loss problems. These problems involve two profit percentages for two parts of a total sale.

How do I calculate the mean price if the ratio is given?

To find the price, use a weighted-average formula. You calculate this by multiplying each item's quantity by its price. Then you add all these prices together. After that, you divide this sum by the quantity of the mixture.

Is alligation applicable to simple-interest problems?

Absolutely. When you put money into two things with different interest rates and you know the total interest rate, you can use a method called 'alligation'. It helps you figure out how much of each investment you have.

What is the most common mistake in SSC mixture and alligation questions?

The biggest mistake is using the selling price or cost instead of the cost price when working with the alligation cross. They should always change the selling price to the cost price before they start solving the problem.