{"id":4596,"date":"2026-09-08T16:10:01","date_gmt":"2026-09-08T10:40:01","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=4596"},"modified":"2026-09-08T16:33:09","modified_gmt":"2026-09-08T11:03:09","slug":"ratio-and-proportion-questions-for-cat-2026-with-solutions","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/ratio-and-proportion-questions-for-cat-2026-with-solutions\/","title":{"rendered":"Ratio and Proportion Questions for CAT 2026: With Solutions"},"content":{"rendered":"\n

Ratio and Proportion questions show up in almost every CAT slot \u2014 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.<\/p>\n\n\n\n

This guide covers the core concepts, solved questions across difficulty levels, common traps, and a free PDF to practice offline.<\/p>\n\n\n\n

Table of Contents<\/h2>\n\n\n\n
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  1. Why Ratio & Proportion Matters for CAT 2026<\/a><\/li>\n\n\n\n
  2. Core Concepts & Formulas<\/a><\/li>\n\n\n\n
  3. Solved Questions: Easy to Difficult<\/a><\/li>\n\n\n\n
  4. Shortcuts to Solve Faster<\/a><\/li>\n\n\n\n
  5. Common Mistakes to Avoid<\/a><\/li>\n\n\n\n
  6. How to Practice This Topic Effectively<\/a><\/li>\n\n\n\n
  7. Key Takeaways<\/a><\/li>\n\n\n\n
  8. FAQs<\/a><\/li>\n<\/ol>\n\n\n\n

    Why Ratio & Proportion Matters for CAT 2026<\/h2>\n\n\n\n

    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 \u2014 since DI sets are often just ratios dressed up as tables and graphs.<\/p>\n\n\n\n

    QA Topic Cluster<\/th>Approx. Weightage<\/th>Ratio & Proportion’s Role<\/th><\/tr><\/thead>
    Arithmetic<\/td>~40%<\/td>Ratio & Proportion is a core sub-topic (2-3 direct questions)<\/td><\/tr>
    Algebra<\/td>~30%<\/td>Ratio-based equations appear in mixture\/age problems<\/td><\/tr>
    Geometry & Mensuration<\/td>~15%<\/td>Similar triangles and scale problems use ratio logic<\/td><\/tr>
    Number System<\/td>~8%<\/td>Ratio-based divisibility questions occasionally appear<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    For the complete section-wise breakdown, see our CAT Quants Syllabus 2026 with topic-wise weightage<\/mark><\/a>.<\/p>\n\n\n\n

    Core Concepts & Formulas You Must Know<\/h2>\n\n\n\n

    What Is a Ratio?<\/h3>\n\n\n\n

    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 \u2014 and it’s the fastest way to solve most CAT ratio problems.<\/p>\n\n\n\n

    What Is a Proportion?<\/h3>\n\n\n\n

    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\u00d7d = b\u00d7c.<\/p>\n\n\n\n

    Concept<\/th>Formula<\/th>When to Use<\/th><\/tr><\/thead>
    Basic Ratio<\/td>a:b = a\/b<\/td>Comparing two quantities directly<\/td><\/tr>
    Proportion<\/td>a:b = c:d \u27f9 ad = bc<\/td>Solving for an unknown term<\/td><\/tr>
    Continued Proportion<\/td>a:b = b:c \u27f9 b\u00b2 = ac<\/td>Three quantities in a chain relationship<\/td><\/tr>
    Componendo-Dividendo<\/td>If a\/b = c\/d, then (a+b)\/(a\u2212b) = (c+d)\/(c\u2212d)<\/td>Simplifying complex ratio equations quickly<\/td><\/tr>
    Combining Ratios<\/td>a:b and b:c \u27f9 a:b:c = (a\u00d7b’):(b\u00d7b’… scaled to common b)<\/td>Merging two separate ratios into one<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Real-World Grounding: Ratios Aren’t Just Exam Tricks<\/h3>\n\n\n\n

    The exact same logic CAT tests is used to compute India’s sex ratio and population statistics published by the Census of India<\/mark><\/a>, and to express core financial indicators \u2014 like the Cash Reserve Ratio or Statutory Liquidity Ratio \u2014 that the Reserve Bank of India<\/mark><\/a> 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.<\/p>\n\n\n\n

    Also Read: CAT Quants Syllabus 2026: The Complete Roadmap<\/mark><\/a><\/em><\/p>\n\n\n\n

    Solved Ratio & Proportion Questions: Easy to Difficult<\/h2>\n\n\n\n

    Easy Level<\/h3>\n\n\n\n

    Q1.<\/strong> The ratio of two numbers is 3:5. If 4 is added to both, the ratio becomes 2:3. Find the numbers.<\/p>\n\n\n\n

    Solution:<\/em> Let the numbers be 3k and 5k. (3k + 4)\/(5k + 4) = 2\/3 \u27f9 9k + 12 = 10k + 8 \u27f9 k = 4 Numbers = 12 and 20.<\/strong><\/p>\n\n\n\n

    Q2.<\/strong> Divide \u20b91,760 among A, B, and C in the ratio 4:5:7.<\/p>\n\n\n\n

    Solution:<\/em> Total parts = 4+5+7 = 16. Value per part = 1760\/16 = \u20b9110. A = \u20b9440, B = \u20b9550, C = \u20b9770.<\/strong><\/p>\n\n\n\n

    Moderate Level<\/h3>\n\n\n\n

    Q3.<\/strong> 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.<\/p>\n\n\n\n

    Solution:<\/em> Let milk = 5k, water = 2k. 5k\/(2k + 14) = 5\/4 \u27f9 20k = 10k + 70 \u27f9 k = 7 Milk = 35 litres.<\/strong><\/p>\n\n\n\n

    Q4.<\/strong> The incomes of X and Y are in the ratio 8:5, and their expenditures are in the ratio 5:3. If each saves \u20b91,000, find X’s income.<\/p>\n\n\n\n

    Solution:<\/em> Let income = 8k, 5k; expenditure = 5m, 3m. Savings: 8k \u2212 5m = 1000 and 5k \u2212 3m = 1000. Solving simultaneously: multiply the first by 3 and second by 5 \u2192 24k \u2212 15m = 3000; 25k \u2212 15m = 5000. Subtract: k = 2000. X’s income = 8 \u00d7 2000 = \u20b916,000.<\/strong><\/p>\n\n\n\n

    Difficult (CAT-Level, TITA Style)<\/h3>\n\n\n\n

    Q5.<\/strong> 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 \u20b969,000, find A’s share.<\/p>\n\n\n\n

    Solution:<\/em> Use investment \u00d7 time. A: (2\u00d74) + (4\u00d78) = 8 + 32 = 40 B: 3\u00d712 = 36 C: 5\u00d712 = 60 Ratio = 40:36:60 = 10:9:15 \u2192 total = 34 parts. A’s share = (10\/34) \u00d7 69000 = \u20b920,294 (approx.)<\/strong><\/p>\n\n\n\n

    Q6.<\/strong> 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?<\/p>\n\n\n\n

    Solution:<\/em> Let numbers = 4k, 7k. (4k+12)\/(7k+12) = 5\/8 \u27f9 32k + 96 = 35k + 60 \u27f9 k = 12 Numbers = 48 and 84; sum = 132.<\/strong><\/p>\n\n\n\n

    For more solved arithmetic problems beyond this topic, see our Top Arithmetic Questions to Practice for CAT 2026<\/mark><\/a>.<\/p>\n\n\n\n

    Shortcuts to Solve Ratio Questions Faster<\/h2>\n\n\n\n
    Situation<\/th>Shortcut<\/th>Saves Time By<\/th><\/tr><\/thead>
    “Ratio becomes X:Y after adding\/subtracting a value”<\/td>Always assume original quantities as ak, bk \u2014 never assign separate variables<\/td>Avoiding two-variable algebra<\/td><\/tr>
    Combining two ratios with a common term<\/td>Scale both ratios so the common term matches (LCM method)<\/td>Skipping fraction-heavy substitution<\/td><\/tr>
    Investment\/partnership problems<\/td>Convert everything to (Investment \u00d7 Time) before taking any ratio<\/td>Prevents the single most common CAT trap<\/td><\/tr>
    Answer options given (MCQ)<\/td>Back-solve using options before setting up equations<\/td>Cuts solving time by 30-40% on select questions<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n


    Don’t just read the solutions\u2014test yourself with our Ratio & Proportion Questions for CAT PDF. Download the free practice PDF and solve additional CAT-level questions at your own pace.<\/mark><\/strong><\/em><\/p>\n\n\n\n

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    DOWNLOAD PDF<\/strong><\/a><\/div>\n<\/div>\n\n\n\n

    Common Mistakes Students Make<\/h2>\n\n\n\n