CAT Mixture and Alligation Questions with Solutions

CAT Mixture and Alligation: Mixture and Alligation questions are very important for the Quantitative Ability section in the Common Admission Test (CAT), which is needed for MBA students in India. This topic looks at how to mix different substances or solutions to get the right ratios or strengths.

• The main idea of Mixture and Alligations is to use ratios, proportions, and averages. Students often need to find out how to mix different parts to make a mixture with specific qualities. This can include problems about simple mixtures, cost mixtures, and mixing alcohol with water.

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Mixtures and Alligation for CAT Preparation

What are Mixtures and Alligation?

Mixtures involve combining two or more substances to create a new mixture with specific properties. Alligation , on the other hand, is a method used to find the ratio in which two or more ingredients at different prices or qualities must be mixed to achieve a desired average price or quality.

Importance of CAT Mixture and Alligation Question

Types of Mixture and Alligation Questions

1. Simple Mixtures: These questions involve mixing two or more substances with different prices or qualities.
   • Example: Mixing milk and water to achieve a desired concentration.
2. Price and Cost Mixtures: Candidates calculate the cost of the mixture or determine the selling price based on given conditions.
   • Example: Finding the price per liter of a mixture of two paints.
3. Alcohol-Water Mixtures: These questions deal with mixing alcohol and water in specific ratios.
   • Example: Determining how much water to add to achieve a certain alcohol concentration.
4. Alligation Questions: Involve determining the ratio in which components should be mixed.
   • Example: Finding the ratio of two solutions needed to obtain a specific concentration.

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Strategies for Solving Mixture and Alligation Questions

1. Set Up Equations: Use algebraic equations based on given information to represent the mixtures.
2. Alligation Formula: Utilize the alligation formula to find required ratios:
   Ratio=Difference between Mean and Lower Price ​
3. Weighted Averages: Apply weighted averages when dealing with mixtures of different concentrations.
4. Simplifying Ratios: Simplify complex ratios by finding common factors or using cross-multiplication.
5. Double Alligation Techniques: For problems involving more than two components, apply double alligation techniques.
6. Consistency Check: After solving, verify if the final ratios or percentages make sense contextually.

Sample Questions with Solutions

Question 1

Solution:

• Initial amounts: Milk = 45×15=12 5 4 ​ × 15 = 12 liters, Water = 15×15=3 5 1 ​ × 15 = 3 liters.
• Let $x$ liters be replaced with pure milk.
• New amount of milk = $12-x+x=12$ liters.
• New amount of water = $3-x$ liters.
• Set up the equation:

• Solve for $x$ :

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Question 2

Solution:

• Initial mixture: Water = 20 liters, Milk = 80 liters.
• Total mixture = $20+80=100$ liters.
• Sold amount = 14×100=25 4 1 ​ × 100 = 25 liters.
• Remaining mixture = $100-25=75$ liters.
• Remaining water proportion:

• Milk remains unchanged at $80$ liters.
• New proportion:

Resources for Practice

• CAT Mixture and Alligation Questions with Solutions PDF Free Download : A comprehensive collection that includes various types of questions encountered in previous exams.
• Mixture and Alligation CAT Previous Year Questions : This resource offers insights into frequently asked questions that can help candidates understand patterns and difficulty levels.
• CAT Arithmetic Questions PDF : This includes a section dedicated specifically to mixtures and alligations, providing ample practice material.

Mixtures and Alligation: Additional Resources