CV
Sign in

CA Foundation · Quantitative Aptitude (Maths, LR, Stats)

Ratio, Proportion, Indices and Logarithms

Chapter 1 · 5 formulas · 4 exam-critical pointers

Core concepts

  1. 01Ratio: comparison of two quantities of same kind in simplest form.
  2. 02Proportion: equality of two ratios; a:b = c:d ⇒ ad = bc.
  3. 03Indices laws: aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ/aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ.
  4. 04Logarithms: if aˣ = N then log_a N = x.
  5. 05Common log (base 10), natural log (base e).

Flowchart

Ratio a:b | Compounded -> ac:bd Duplicate -> a²:b² Sub-dup -> √a:√b | v Proportion: a:b :: c:d

Exam-critical pointers

  • ⭐Duplicate ratio of a:b = a²:b². Sub-duplicate = √a:√b.
  • ⭐Watch unit consistency — convert to same unit before forming ratio.
  • ⭐Antilog: anti(log x) = 10ˣ for common log.
  • ⭐ICAI loves 2-mark direct application MCQs from log tables.

Make it click