Ratio and Proportion is an important topic in quantitative aptitude. Questions from this topic are less time-consuming and easy to solve. In this blog, we have provided the key formulas to solve ratio and proportion questions, along with short tricks and strategies.
What Is Ratio and Proportion in Quantitative Aptitude?
Ratio is a comparison of two quantities using division. It shows how many times one quantity is contained in another.
Proportion states that two ratios are equal. It is a statement showing equivalence of two ratios.
This topic appears in exams because it tests basic arithmetic reasoning, logical comparison, and problem-solving speed, especially in financial and commercial scenarios.
Skills required:
- Logical comparison
- Fast simplification
- Applying inverse/compound ratio techniques
Why Is Ratio and Proportion Important in Competitive Exams?
One to two questions always come from this topic, which are easy to solve and less time-consuming. The details of the number of questions asked from this topic are as follows:
| Exam | No. of Questions | Difficulty |
| SSC CGL / CHSL | 1–2 | Easy |
| IBPS PO / SBI PO | 1–2 | Moderate |
| RRB NTPC / Group D | 1 | Easy |
| State PSC / Police | 1–2 | Moderate |
Terms Used in Ratio and Proportion Questions
The terms that are commonly used to solve questions based on ratio and proportion are as follows:
| Term | Explanation |
| Ratio (a : b) | Comparison between two quantities (a is to b) |
| Proportion (a : b = c : d) | Two ratios are said to be in proportion; a/b = c/d |
| Cross Multiplication | If a/b = c/d, then a × d = b × c |
| Continued Proportion | If a : b = b : c, then b is the mean proportional |
| Mean Proportion | Mean of two numbers a and b is √(ab) |
| Third Proportion | If a : b = b : c, then c is the third proportion |
| Duplicate Ratio | The ratio of squares: a² : b² |
| Inverse Ratio | When the product of elements is constant; reverse relationship |
| Compound Ratio | Resultant of multiplying two or more ratios: ac : bd |
| Equivalent Ratios | Ratios that represent the same relationship, e.g., 2:4 = 1:2 |
What Are the Types of Ratio and Proportion Questions in Quantitative Aptitude?
Types of questions that are asked in ratio and proportion are as follows:
- Direct Ratio Problems: Straightforward comparison
- Proportion-based Word Problems: “If A : B = 2:3 and B : C = 4:5, find A : C”
- Mixture & Partnership Problems: Based on proportional shares
- Time-Work/Money Ratios: Embedded in compound problem statements
- Inverse Ratio: Scenarios involving speed-time or men-work questions
Ratio and Proportion Formulas for Quantitative Aptitude
Formulas used to solve ratio and proportion questions are as follows:
Ratio and Proportion Tricks for SSC CGL and Other Exams
Tricks to solve ratio and proportion quantitative aptitude questions are as follows:
- Convert all ratios into fractions for faster simplification
- Use cross-multiplication to verify proportionality
- Combine ratios step-by-step for chain ratio problems
- Remember standard triples: 2:3:4, 3:4:5
- In partnership/money questions, treat ratio as share units
- For reverse calculations, use inverse ratio directly
Solved Ratio and Proportion Questions from 2024–25 Exams
Question 1:
Asked in SSC CGL 2024 Tier 1 Shift 2 – Memory-Based
If A : B = 3:5 and B : C = 2:7, find A : B : C.
Answer:
A : B = 3:5
B : C = 2:7
Make B common: LCM of 5 and 2 = 10
A:B = 6:10, B:C = 10:35 → A:B:C = 6:10:35
Question 2:
From IBPS PO Prelims 2024 – Memory Based
A sum of ₹8400 is divided between A and B in the ratio 5:2. What is B’s share?
Answer:
Total parts = 5 + 2 = 7
B’s share = 27×8400=₹2400\frac{2}{7} \times 8400 = ₹240072×8400=₹2400
Question 3:
Asked in RRB NTPC 2024 – Memory-Based
If a:b = 4:5 and b:c = 6:7, find a:c.
Answer:
a:b = 4:5, b:c = 6:7
Make b common (LCM of 5 and 6 = 30)
a:b = 24:30, b:c = 30:35 → a:c = 24:35
Ratio and Proportion Concepts for Bank Exams
Bank exams often include compound ratios, time-work based proportions, or profit-loss proportions.
Example:
A and B invest in a business in the ratio 5:4. After 8 months, C joins and the profit is divided in the ratio 20:16:9. Find for how many months C invested.
→ Use ratio × time = share for each partner and solve proportionally.
Common Mistakes to Avoid while Solving Ratio and Proportion
While solving Ratio and Proportion Quantitative Aptitude questions, candidates must keep the below points in mind:
- Confusing proportion with percentage comparison
- Not equalizing common terms before combining ratios
- Dividing incorrectly while distributing quantities
- Skipping units (Rs, kg, hrs) in word problems
- Failing to reduce ratios to their simplest form before solving
What Are Related Topics I Should Revise Next?
Topics you should revise next are as follows:
- Questions based on Time and Distance
- Rules and Practice Questions of Simplification
- Shortcuts and Patterns of Number Series
- Various types of Questions Based on Data Interpretation
- Tricks & Examples of Inequalities
FAQs
A ratio compares two quantities, while proportion states that two ratios are equal.
If a : b = b : c, then c is the third proportion, calculated as c = b² / a.
Multiply corresponding terms directly: (a : b) × (c : d) = ac : bd.
Yes, simplifying helps avoid calculation mistakes and makes comparisons easier.
Mixing up terms, incorrect cross multiplication, and wrong unit assumptions.
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