Ratio and Proportion questions show up in almost every CAT slot — yet most aspirants either rush through them carelessly or overthink what’s actually a fairly mechanical topic. Get the basics right, and this becomes one of the fastest-scoring areas in the entire QA section.
This guide covers the core concepts, solved questions across difficulty levels, common traps, and a free PDF to practice offline.
Table of Contents
- Why Ratio & Proportion Matters for CAT 2026
- Core Concepts & Formulas
- Solved Questions: Easy to Difficult
- Shortcuts to Solve Faster
- Common Mistakes to Avoid
- How to Practice This Topic Effectively
- Key Takeaways
- FAQs
Why Ratio & Proportion Matters for CAT 2026
Ratio and Proportion sits inside Arithmetic, which alone accounts for roughly 40% of the QA section. Within that cluster, this specific topic usually contributes 2-3 direct questions, and quietly supports several Averages, Mixtures, and Data Interpretation sets too — since DI sets are often just ratios dressed up as tables and graphs.
| QA Topic Cluster | Approx. Weightage | Ratio & Proportion’s Role |
|---|---|---|
| Arithmetic | ~40% | Ratio & Proportion is a core sub-topic (2-3 direct questions) |
| Algebra | ~30% | Ratio-based equations appear in mixture/age problems |
| Geometry & Mensuration | ~15% | Similar triangles and scale problems use ratio logic |
| Number System | ~8% | Ratio-based divisibility questions occasionally appear |
For the complete section-wise breakdown, see our CAT Quants Syllabus 2026 with topic-wise weightage.
Core Concepts & Formulas You Must Know
What Is a Ratio?
A ratio compares two quantities of the same kind. If A and B are in the ratio a:b, it simply means A = ak and B = bk for some constant k. That constant is the part most students forget to use — and it’s the fastest way to solve most CAT ratio problems.
What Is a Proportion?
A proportion states that two ratios are equal: a:b = c:d, or equivalently a/b = c/d. This gives the classic rule “product of extremes = product of means,” i.e., a×d = b×c.
| Concept | Formula | When to Use |
|---|---|---|
| Basic Ratio | a:b = a/b | Comparing two quantities directly |
| Proportion | a:b = c:d ⟹ ad = bc | Solving for an unknown term |
| Continued Proportion | a:b = b:c ⟹ b² = ac | Three quantities in a chain relationship |
| Componendo-Dividendo | If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d) | Simplifying complex ratio equations quickly |
| Combining Ratios | a:b and b:c ⟹ a:b:c = (a×b’):(b×b’… scaled to common b) | Merging two separate ratios into one |
Real-World Grounding: Ratios Aren’t Just Exam Tricks
The exact same logic CAT tests is used to compute India’s sex ratio and population statistics published by the Census of India, and to express core financial indicators — like the Cash Reserve Ratio or Statutory Liquidity Ratio — that the Reserve Bank of India uses to set monetary policy. If you can grasp how these real bodies compute and interpret ratios, the exam version becomes almost trivial by comparison.
Also Read: CAT Quants Syllabus 2026: The Complete Roadmap
Solved Ratio & Proportion Questions: Easy to Difficult
Easy Level
Q1. The ratio of two numbers is 3:5. If 4 is added to both, the ratio becomes 2:3. Find the numbers.
Solution: Let the numbers be 3k and 5k. (3k + 4)/(5k + 4) = 2/3 ⟹ 9k + 12 = 10k + 8 ⟹ k = 4 Numbers = 12 and 20.
Q2. Divide ₹1,760 among A, B, and C in the ratio 4:5:7.
Solution: Total parts = 4+5+7 = 16. Value per part = 1760/16 = ₹110. A = ₹440, B = ₹550, C = ₹770.
Moderate Level
Q3. A mixture contains milk and water in the ratio 5:2. If 14 litres of water is added, the ratio becomes 5:4. Find the initial quantity of milk.
Solution: Let milk = 5k, water = 2k. 5k/(2k + 14) = 5/4 ⟹ 20k = 10k + 70 ⟹ k = 7 Milk = 35 litres.
Q4. The incomes of X and Y are in the ratio 8:5, and their expenditures are in the ratio 5:3. If each saves ₹1,000, find X’s income.
Solution: Let income = 8k, 5k; expenditure = 5m, 3m. Savings: 8k − 5m = 1000 and 5k − 3m = 1000. Solving simultaneously: multiply the first by 3 and second by 5 → 24k − 15m = 3000; 25k − 15m = 5000. Subtract: k = 2000. X’s income = 8 × 2000 = ₹16,000.
Difficult (CAT-Level, TITA Style)
Q5. Three partners A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A doubles his investment. If the total profit at year-end is ₹69,000, find A’s share.
Solution: Use investment × time. A: (2×4) + (4×8) = 8 + 32 = 40 B: 3×12 = 36 C: 5×12 = 60 Ratio = 40:36:60 = 10:9:15 → total = 34 parts. A’s share = (10/34) × 69000 = ₹20,294 (approx.)
Q6. Two numbers are in the ratio 4:7. If each is increased by 12, the ratio becomes 5:8. What is the sum of the original numbers?
Solution: Let numbers = 4k, 7k. (4k+12)/(7k+12) = 5/8 ⟹ 32k + 96 = 35k + 60 ⟹ k = 12 Numbers = 48 and 84; sum = 132.
For more solved arithmetic problems beyond this topic, see our Top Arithmetic Questions to Practice for CAT 2026.
Shortcuts to Solve Ratio Questions Faster
| Situation | Shortcut | Saves Time By |
|---|---|---|
| “Ratio becomes X:Y after adding/subtracting a value” | Always assume original quantities as ak, bk — never assign separate variables | Avoiding two-variable algebra |
| Combining two ratios with a common term | Scale both ratios so the common term matches (LCM method) | Skipping fraction-heavy substitution |
| Investment/partnership problems | Convert everything to (Investment × Time) before taking any ratio | Prevents the single most common CAT trap |
| Answer options given (MCQ) | Back-solve using options before setting up equations | Cuts solving time by 30-40% on select questions |
Don’t just read the solutions—test yourself with our Ratio & Proportion Questions for CAT PDF. Download the free practice PDF and solve additional CAT-level questions at your own pace.
Common Mistakes Students Make
- Forgetting the constant “k”: Treating a:b as literal values instead of ak:bk leads to wrong equations almost every time.
- Ignoring time in partnership problems: Skipping the time-weighting step (like in Q5) is the single most common reason ratio-based profit-sharing questions go wrong.
- Mixing up mean and extremes in the proportion rule — always double-check which terms multiply together.
- Rushing TITA questions: Since there are no options to sanity-check against, small arithmetic slips go unnoticed until it’s too late.
How to Practice This Topic Effectively
Reading solutions isn’t the same as solving under time pressure. Once you’re comfortable with the concepts above, move to timed sectional practice so you build both speed and accuracy. Test and Strengthen your overall performance with Free Full-Length CAT Mock Tests.
For candidates who want to revisit the fundamentals from school-level maths first, the NCERT Class 8 mathematics textbook covers ratio and proportion in a simplified, structured format that’s a genuinely useful refresher before jumping into CAT-level difficulty.
Key Takeaways
- Ratio & Proportion contributes 2-3 direct QA questions and quietly supports Averages, Mixtures, and DI sets too.
- Always introduce a constant “k” when working with ratios — it turns most problems into single-variable equations.
- Partnership and investment ratio questions require weighting by time, not just capital.
- Use the componendo-dividendo shortcut and back-solving from options to save time on exam day.
- Concept clarity plus timed sectional practice — not just formula memorization — is what converts this topic into consistent marks.
Frequently Asked Questions
How many Ratio and Proportion questions come in CAT?
CAT typically includes 2-3 direct questions on Ratio and Proportion within the Arithmetic cluster of QA, though the concept also appears indirectly in Averages, Mixtures, and several Data Interpretation sets.
Is Ratio and Proportion an easy topic for CAT?
Yes, relative to other QA topics, Ratio and Proportion is considered easy-to-moderate in difficulty. Most questions are formula-based rather than concept-heavy, which makes it one of the highest-ROI topics to master early in your preparation.
What is the difference between ratio and proportion?
A ratio compares two quantities of the same kind (a:b), while a proportion states that two such ratios are equal (a:b = c:d). In simple terms, a proportion is an equation made up of two ratios.
Which formula is most important for CAT Ratio and Proportion questions?
The componendo-dividendo rule — if a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d) — is disproportionately useful because it quickly simplifies complex ratio equations that would otherwise require lengthy algebra.
How should I practice Ratio and Proportion for CAT 2026?
Start by mastering the constant-k method on basic problems, then move to partnership and mixture-based questions that combine ratio logic with other concepts, and finally attempt timed sectional QA mocks to build speed under exam conditions.
Conclusion
Ratio and Proportion rewards preparation more than raw talent — once the constant-k approach and the shortcuts above are second nature, these questions become some of the fastest marks available in the QA section. Work through the solved examples again without looking at the solutions, download the practice PDF for additional questions, and follow it up with a timed sectional mock to see where you actually stand.
External Source: Ministry of Education, Government of India — higher education policy and exam-recognition framework
You May Also Like : CAT MOCK, CAT MOCK PYQ
Follow Us On : Facebook, Instagram, Youtube
