Alligation or Mixture
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Cheat Sheets
Study MaterialAlligation and Mixture Cheat Sheet
Alligation and Mixture is one of the most important arithmetic topics in Quantitative Aptitude and is frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, and other competitive examinations.
This cheat sheet helps candidates understand mixture concepts, alligation rules, mean price calculations, replacement problems, alloy mixtures, and shortcut techniques for solving alligation and mixture questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Alligation and Mixture for competitive exams:
Basic Concepts
- Mixture Concepts
- Combining Ingredients
- Mean Price
- Weighted Average Concept
Alligation Rule
- Cheaper : Dearer Ratio
- Mean Price Formula
- Cross Difference Method
- Ratio Calculation Tricks
Mixture Cost Problems
- Mixing Two Varieties
- Cost Price of Mixture
- Quantity Calculations
- Profit Percentage Problems
Replacement Problems
Problems involving removing and replacing part of the mixture repeatedly.
Milk & Water Problems
- Water Mixed with Milk
- Percentage of Water
- Repeated Replacement
- Purity Problems
Alloys & Metal Mixtures
- Mixing Metals
- Alloy Ratio Problems
- Gold & Silver Mixtures
- Purity Calculations
Practical Applications
- Tea, Rice & Sugar Mixtures
- Alcohol & Water Problems
- Business Profit Mixtures
- Repeated Mixing Concepts
Shortcut Tricks
Fast solving methods, alligation shortcuts, and exam-oriented arithmetic techniques.
Topics Covered
| Topic | Description |
|---|---|
| Mixture Concept | Combining two or more ingredients |
| Alligation Rule | Ratio finding method for mixtures |
| Mean Price | Average price of mixture |
| Mixture Cost | Finding cost of mixed ingredients |
| Quantity Problems | Finding quantities in mixture |
| Replacement Problems | Removing and replacing mixture repeatedly |
| Repeated Replacement Formula | Formula for remaining original quantity |
| Milk & Water Problems | Percentage and purity calculations |
| Alloy Problems | Mixing metals and alloys |
| Alcohol & Water Problems | Liquid mixture calculations |
| Profit in Mixture | Profit percentage calculations in mixtures |
| Tea & Rice Mixtures | Commercial mixture problems |
| Repeated Mixing | Multiple replacement operations |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Mixture Concepts
↓
Improve Arithmetic Skills
↓
Apply Shortcut Techniques
↓
Solve Mixture Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Examples
Example 1:
Rice costing ₹20/kg is mixed with rice costing ₹30/kg to form a mixture costing ₹24/kg. Find the ratio of quantities.
Using Alligation:
Cheaper : Dearer
= (30 − 24) : (24 − 20)
= 6 : 4
= 3 : 2
Example 2:
A vessel contains 40 liters milk. 10 liters are removed and replaced with water. Find fraction of milk left.
Milk remaining =
1 − 10/40
= 3/4
Milk left = 30 liters
Example 3:
Find the mean price of tea mixed in ratio 2:3 costing ₹40/kg and ₹55/kg respectively.
Mean Price =
(2×40 + 3×55) / 5
= (80 + 165)/5
= ₹49/kg
Example 4:
A merchant mixes 20 liters water with 80 liters milk. Find percentage of water in mixture.
Total mixture = 100 liters
Water percentage =
20/100 × 100
= 20%
Example 5:
Gold and silver are mixed in ratio 3:2. Find quantity of silver in 50 grams alloy.
Total ratio = 5
Silver quantity =
2/5 × 50
= 20 grams
Final Takeaway
This Alligation and Mixture Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of alligation rules, replacement problems, alloy mixtures, and shortcut techniques can significantly improve speed, accuracy, and arithmetic problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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