Ratio and Proportion Questions for SBI PO Mains is a fundamental and high-yield topic in the Quantitative Aptitude and Data Analysis section. Questions are generally moderate to difficult and are often integrated with percentage, profit and loss, partnership, mixture, ages, time and work, and data interpretation. To strengthen your preparation, practise concept-based questions, attempt timed interactive assessments, and use targeted study material to master the shortcuts and applications needed to solve complex Mains-level quizzes.
Ratio and Proportion Questions for SBI PO Mains: Attempt LIVE Quiz
Test your speed and accuracy with these 10 exam-pattern live practice questions curated for SBI PO Mains 2026. Solve them within a timed environment before checking the detailed solutions at the end of the article.
Q1. Incomes of A and B are in the ratio 5:7, and their expenditures are in the ratio 3:5. If A saves ₹4,000 and B saves ₹2,000, find their total combined income.
Explanation: Let incomes be 5x and 7x. Then expenditures are 5x−4000 and 7x−2000. So (5x−4000)/(7x−2000)=3/5. Solving gives x=3500. Combined income=12x=₹42,000.
Q2. A vessel contains milk and water in the ratio 7:5. Nine litres of mixture are removed and replaced with pure water, after which the ratio becomes 7:9. What was the original capacity?
Explanation: Let capacity be V. Milk remaining after removing 9 litres is 7/12×(V−9). Final milk fraction is 7/16, so 7/12×(V−9)=7/16×V. Hence V=36 litres.
Q3. A, B and C enter a partnership. A invests 3 times B, and B invests 2/3 of C. Total profit is ₹6,600. Find B's share.
Explanation: Let C=3x, then B=2x and A=6x. Ratio A:B:C=6:2:3. B's share=2/11×6600=₹1,200.
Q4. Four years ago, the ratio of ages of A and B was 4:5. Eight years from now, the ratio will be 11:13. Find B's present age.
Explanation: Let ages four years ago be 4x and 5x. Then eight years from now they are 4x+12 and 5x+12. (4x+12)/(5x+12)=11/13 gives x=8. So B's present age=5x+4=44 years.
Q5. Find the third proportional to 16 and 24.
Explanation: 16:24=24:c, so c=24²/16=36.
Q6. A bag contains 50p, 25p and 10p coins in the ratio 5:9:4, with total value ₹206. Find the total number of coins.
Explanation: Let counts be 5x,9x,4x. Total value=5x×0.50+9x×0.25+4x×0.10=5.15x=206, so x=40. Total coins=18x=720.
Q7. Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio becomes 12:23. Find the smaller original number.
Explanation: Let numbers be 3x and 5x. (3x−9)/(5x−9)=12/23 gives x=11. Smaller number=33.
Q8. If A:B=2:3, B:C=4:5 and C:D=6:7, find A:B:C:D.
Explanation: Combine A:B and B:C to get 8:12:15. Match C with 6:7 by scaling to 30, giving A:B:C:D=16:24:30:35.
Q9. In a regiment, officers:soldiers=3:31. After 6 officers and 22 soldiers are killed, the ratio becomes 1:13. Find the original number of officers.
Explanation: Let officers=3x and soldiers=31x. (3x−6)/(31x−22)=1/13 gives x=7. Original officers=21.
Q10. Monthly incomes of P and Q are in the ratio 4:3 and expenses in the ratio 3:2. If each saves ₹6,000, find P's monthly income.
Explanation: Let incomes be 4x and 3x, expenses 3y and 2y. Then 4x−3y=6000 and 3x−2y=6000. Subtracting gives x=y; hence x=6000 and P's income=₹24,000.
Quiz Summary
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Solve More QuestionsBenefits of Attempting Ratio and Proportion Live Quizzes for Bank Mains
Practicing advanced ratio questions in a timed live quiz setting provides strategic advantages tailored for banking aspirants:
- Eliminates Monotonous Calculation Errors: Mains DI sets involve large numbers. Using ratio unit assignments minimizes multi-digit multiplications.
- Improves Question Selection Skills: As expert banking mentors emphasize, “SBI PO Mains is defined by which questions you skip rather than which you attempt.” Live quizzes teach strategic selection.
- Enhances Data Interpretation Speed: Converting complex percentage graphs and funnel charts into ratio multipliers boosts DI speed by up to 40%.
- Seamless Integration with Other Topics: Ratios directly power [Mixtures, Alligations & Partnership] and [Time & Work Efficiency] problems.
Core Concepts, High-Yield Formulas, and Shortcut Tricks for SBI PO Mains
SBI PO Mains requires deep clarity on high-yield arithmetic relationships. Review the core breakdown below:
| Concept Category | What to Learn / Application | Key Formula / Shortcut |
| Basic Proportion | Mean, Third, and Fourth Proportional | Mean = √(a × b); Third = b² / a; Fourth = (b × c) / a |
| Cross-Multiplication Method | Skip linear equations for age/income shifts | Compare initial & final ratios with difference additions |
| Partnership & Profit | Distributing profits over variable periods | Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂) |
| Mixture Replacement | Repeated liquid replacement iterations | Remaining / Original = (1 − x/V)ⁿ |
| Direct & Inverse Variation | Speed-time & work-efficiency relations | Direct: x₁/x₂ = y₁/y₂ | Inverse: x₁y₁ = x₂y₂ |
High-Yield Pro Tip for SBI PO Mains: Fractional Equivalencing
Convert complex percentages to simple fractional ratios immediately! For example, an increase of 37.5% means multiplying by 11/8 (since 37.5% = 3/8). Utilizing unit scaling (1 part = x) avoids setting up lengthy algebraic expressions under exam pressure.
How to Prepare Ratio and Proportion Questions for Bank Exams?
- Build Unshakable Conceptual Clarity: Start by completing comprehensive video marathons by expert faculties (such as Kaushik Sir, Ashish Sir, Harshal Sir, or Yashraj Sir). Focus on understanding fundamental ratio properties over memorizing formulas.
- Solve High-Level Topic PDFs: Transition from basic questions to Mains-level topic bundles (such as Guidely or Smartkeeda PDF sets) covering multi-variable word problems.
- Master Unit-Ratio & Cross-Multiplication Tricks: Avoid writing full algebraic equations (x and y) where cross-multiplication or unit scaling applies.
- Practice Sectional Mocks & Previous Year Questions (PYQs): Take full-length sectional tests on platforms like Testbook or PracticeMock. Analyze every unattempted or incorrect question in detail.
- Curate Quick Revision Notes: For last-minute brush-ups, maintain compact formula sheets summarizing Speed Maths, Percentages, and Ratio shortcuts. Explore our recommended [Free Quants Speed Revision Notes Collection] for fast-track preparation.
Conclusion
Mastering Ratio and Proportion is an indispensable strategy for clearing the SBI PO Mains cutoff. By moving beyond basic algebraic equations and adopting unit scaling, fractional equivalencing, and strategic question selection, you can drastically boost both accuracy and speed in Quantitative Aptitude. Continue practicing with our live quiz sets, analyze your weak areas, and download free topic notes to secure your dream bank PO career in 2026!
Ratio and Proportion Questions for SBI PO Mains Frequently Asked Questions
Q1. What is the weightage of Ratio and Proportion in SBI PO Mains?
While pure direct ratio questions rarely appear, ratio concepts directly drive 60–70% of Quantitative Aptitude marks through Caselets, DI sets, Mixtures, and Partnerships.
Q2. How does Ratio and Proportion differ between SBI PO Prelims and Mains?
Prelims tests basic execution speed on simple linear equations. Mains tests multi-concept integration, variable-based ratios, and complex data extraction from DI charts.
Q3. What is the cross-multiplication method in ratio questions?
It is a speed technique used to calculate unknown quantities in age or income shifts without writing quadratic or double linear algebraic equations.
Q4. Are free PDFs sufficient for SBI PO Mains Ratio preparation?
Free PDFs provide strong foundational question banks. However, combining PDF practice with timed live quizzes and mock analysis is essential to build exam speed.
Q5. Which topics should I master alongside Ratio and Proportion?
You should concurrently master Percentages, Averages, Mixtures & Alligations, Profit & Loss, and Time & Work for complete Quantitative Aptitude synergy.
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