Ratio and Proportion
📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.
Cheat Sheets
Study MaterialRatio and Proportion Cheat Sheet
Ratio and Proportion is one of the most important and frequently asked topics in Quantitative Aptitude for SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand ratio concepts, proportion properties, partnership problems, mixture questions, direct and inverse proportion, and shortcut methods for solving ratio-based problems quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Ratio and Proportion for competitive exams:
Basic Ratio Concepts
- Ratio Representation (a:b)
- Simplification of Ratios
- Comparison of Ratios
- Equivalent Ratios
Types of Ratios
- Compound Ratio
- Duplicate Ratio
- Triplicate Ratio
- Inverse Ratio
Proportion Basics
- a:b = c:d
- Mean Proportional
- Third Proportional
- Fourth Proportional
Properties of Proportion
Alternendo, invertendo, componendo, dividendo, and componendo-dividendo concepts.
Direct & Inverse Proportion
- Direct Variation
- Inverse Variation
- Work & Time Relation
- Quantity Relationships
Partnership Problems
- Profit Sharing
- Capital & Time Ratio
- Business Investment Problems
- Loss Distribution
Mixture & Distribution Problems
- Mixture Problems
- Distribution of Amount
- Coins & Currency Ratios
- Age Ratio Problems
Shortcut Tricks
Fast solving methods, ratio shortcuts, and exam-oriented proportion techniques.
Topics Covered
| Topic | Description |
|---|---|
| Basic Ratio | Comparison of two quantities using division |
| Simplification of Ratios | Reducing ratios into simplest form |
| Compound Ratio | Ratio obtained by multiplying ratios |
| Duplicate & Triplicate Ratio | Square and cube based ratios |
| Inverse Ratio | Ratio obtained by reversing terms |
| Proportion | Equality of two ratios |
| Mean Proportional | Middle proportional value between two numbers |
| Continued Proportion | Proportional relationship among terms |
| Properties of Proportion | Alternendo, invertendo, componendo, dividendo rules |
| Direct Proportion | Quantities increasing or decreasing together |
| Inverse Proportion | One quantity increases while another decreases |
| Partnership Problems | Profit and loss sharing based on investment |
| Mixture Problems | Mixing two or more ingredients |
| Distribution Problems | Division of amounts in given ratio |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Ratio Concepts
↓
Improve Logical Thinking
↓
Apply Shortcut Techniques
↓
Solve Word 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 Example
Example:
Divide ₹720 between A and B in the ratio 5 : 7.
Total ratio = 5 + 7 = 12
A's share =
(5 ÷ 12) × 720 = ₹300
B's share =
(7 ÷ 12) × 720 = ₹420
Answer:
A = ₹300
B = ₹420
Final Takeaway
This Ratio and Proportion Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of ratio simplification, partnership problems, mixture concepts, direct and inverse proportion, and shortcut techniques can significantly improve speed, accuracy, and analytical 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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