Ratio and Proportion in Quantitative Aptitude is one of the most important and scoring topics in competitive exams like SSC, Banking, Railway, Defence, and various State-level exams. Questions from this chapter frequently appear in arithmetic sections and also form the foundation for advanced topics like Partnership, Mixture & Alligation, Percentage, and Profit & Loss.
Many students feel this topic is tricky, but in reality, Ratio and Proportion is completely logical and formula-based. Once the concepts are clear, you can solve most questions quickly and accurately.
At Informosio, we focus on building strong fundamentals with simple explanations and exam-oriented strategies. In this complete guide, you will learn Ratio and Proportion step by step with formulas, solved examples, shortcut methods, and preparation tips.
What is Ratio?
A ratio is a comparison of two quantities of the same kind.
It shows how many times one quantity is related to another.
If two numbers are a and b, then:
Ratio = a : b
or
a/b
Example 1:
If the number of boys is 20 and girls is 10,
Ratio of boys to girls = 20 : 10
Simplify:
Divide both by 10
= 2 : 1
Important Points About Ratio
- Order matters in ratio.
- 2 : 3 is different from 3 : 2.
- Ratios must be simplified to lowest form.
- Units must be same before forming ratio.
Example 2:
Convert 2 kg and 500 g into ratio.
Convert into same unit:
2 kg = 2000 g
Ratio = 2000 : 500
= 4 : 1
What is Proportion?
When two ratios are equal, they form a proportion.
If:
a : b = c : d
Then,
a/b = c/d
This is called proportion.
Example:
2 : 4 = 3 : 6
2/4 = 3/6
Both equal 1/2
So they are in proportion.
Important Formula in Proportion
If:
a : b = c : d
Then,
a × d = b × c
This is called cross multiplication rule.
Example:
If 3 : x = 6 : 8
Then:
3 × 8 = 6 × x
24 = 6x
x = 4
Types of Ratio
1. Simple Ratio
Direct comparison of two numbers.
Example: 5 : 7
2. Compound Ratio
Combination of two or more ratios.
If:
a : b and c : d
Compound ratio = ac : bd
Example:
2 : 3 and 4 : 5
Compound ratio = (2×4) : (3×5)
= 8 : 15
3. Duplicate Ratio
Duplicate ratio of a : b = a² : b²
Example:
Duplicate ratio of 3 : 5
= 9 : 25
4. Triplicate Ratio
Triplicate ratio of a : b = a³ : b³
Example:
Triplicate ratio of 2 : 3
= 8 : 27
Continued Proportion
If:
a : b = b : c
Then b is called mean proportional.
Formula:
b² = ac
Example:
Find mean proportional between 4 and 9.
b² = 4 × 9
b² = 36
b = 6
Third Proportion
If:
a : b = b : c
Then c is called third proportional.
Formula:
c = b² / a
Fourth Proportion
If:
a : b = c : d
Then d is fourth proportional.
Formula:
d = (b × c) / a
Ratio in Real-Life Problems
Ratio and Proportion are widely used in:
- Age problems
- Partnership
- Mixture & Alligation
- Speed problems
- Percentage
Strong basics here help in many chapters.
Example Problems
Example 1:
The ratio of ages of A and B is 3 : 5. If A is 18 years old, find B’s age.
Let ages be:
3x and 5x
3x = 18
x = 6
So B = 5x = 30 years
Example 2:
Divide ₹1200 in the ratio 2 : 3.
Total parts = 2 + 3 = 5
Value of 1 part = 1200/5 = 240
So:
First share = 2 × 240 = 480
Second share = 3 × 240 = 720
Direct and Inverse Proportion
Direct Proportion
If one quantity increases, the other also increases.
Example:
More workers → more work done
Formula:
x₁ / x₂ = y₁ / y₂
Inverse Proportion
If one increases, the other decreases.
Example:
More workers → fewer days required
Formula:
x₁ × y₁ = x₂ × y₂
Common Mistakes Students Make
- Forgetting to simplify ratio
- Mixing units
- Using wrong proportion formula
- Making calculation errors
- Not identifying direct or inverse proportion
Practice reduces these mistakes.
Preparation Strategy
To master Ratio and Proportion in Quantitative Aptitude:
- Understand basic definitions clearly
- Memorize key formulas
- Practice 15 questions daily
- Solve previous year questions
- Focus on word problems
Consistency improves speed and accuracy.
Why This Topic Is Important
Ratio and Proportion is a foundation chapter. Many advanced arithmetic topics depend on it. If your basics are strong, you can solve complex questions easily.
In exams like SSC and Banking, 2–4 questions are usually asked directly or indirectly from this topic.
Final Conclusion
Ratio and Proportion in Quantitative Aptitude is a logical and formula-based topic. Once you understand the basic concepts and practice regularly, it becomes one of the most scoring chapters in competitive exams.
At Informosio, we recommend focusing on concept clarity first, then practicing daily to improve speed. With proper preparation and consistent effort, you can master this topic confidently.
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