Banking Notes / Quantitative Aptitude / Chapter 6
Chapter 6 of 26

Ratio & Proportion

Compound ratios, proportion rules, and how this topic quietly powers Partnership, Mixture, and DI questions across the paper.

📖 ~8 min read 🏦 Banking Quantitative Aptitude

Introduction

A ratio compares two quantities of the same kind; a proportion states that two ratios are equal. This chapter is rarely tested alone in banking exams but is the backbone of Partnership, Mixture & Alligation, and several DI caselet questions.

Key Rules

RuleStatement
Compounding ratiosa:b and c:d combine to (a×c) : (b×d)
Inverse ratioInverse of a:b is b:a
Duplicate ratioa²:b² is the duplicate ratio of a:b
Sub-duplicate ratio√a : √b
Continued proportiona:b = b:c ⟹ b² = ac (b is the mean proportional)
Q. Divide ₹4,400 among A, B and C in the ratio 2:3:6.
Total parts = 2+3+6 = 11. Each part = 4400/11 = 400. A = 2×400 = ₹800, B = 3×400 = ₹1,200, C = 6×400 = ₹2,400.
Q. If a:b = 3:4 and b:c = 8:9, find a:b:c.
Make the common term (b) equal: a:b = 3:4 = 6:8, and b:c = 8:9. Now b matches at 8. So a:b:c = 6 : 8 : 9.
⚠️ Key Insight: To combine ratios sharing a common term, scale both ratios so that the shared term matches — this avoids fraction-heavy calculation.
💡 Exam Tip: Whenever a DI caselet or Mixture question gives you "in the ratio of," convert directly to parts (as in the ₹4,400 example) instead of setting up algebraic equations — it's faster under time pressure.
✅ Practice Focus: Dividing an amount in a given ratio · Combining two ratios via a common term · Mean proportional problems.

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