Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 5
Chapter 5 of 31

Ratio and Proportion

Comparing quantities and combining ratios — a foundation used throughout Partnership, Mixture & Alligation, and Age problems.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Ratio Basics

  • A ratio a:b compares two quantities of the same kind
  • A ratio has no units and remains unchanged when both terms are multiplied/divided by the same number

Types of Ratios

TypeMeaning
Compound Ratioa: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

Proportion

  • Four quantities a, b, c, d are in proportion if a:b = c:d, written a:b :: c:d
  • Product of extremes = Product of means: a×d = b×c
  • Continued Proportion: a:b = b:c ⟹ b² = a×c (b is the mean proportional)
💡 Example: Divide ₹4,400 among A, B, C in ratio 2:3:6. Total parts = 11; each part = 400. A=₹800, B=₹1,200, C=₹2,400.
💡 To combine two ratios sharing a common term (a:b and b:c), scale both so the shared term matches, then merge into a:b:c.

💡 Want More? Get the Full eBook

This free chapter covers the key concepts. For complete coverage with 500+ MCQs, mock tests, and previous year analysis — grab the premium eBook.

📚 Browse Premium eBooks →