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Notes/CA Foundation/Quantitative Aptitude (Maths, LR, Stats)

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 summary

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

Formula sheet

  • log(mn) = log m + log n
  • log(m/n) = log m − log n
  • log mⁿ = n log m
  • log_a b = log b / log a (change of base)
  • Mean Proportional between a and b = √(ab)

More from Quantitative Aptitude (Maths, LR, Stats)

  1. Ch 2Permutations and Combinations
  2. Ch 3Time Value of Money
  3. Ch 4Measures of Central Tendency & Dispersion
  4. Ch 5Correlation and Regression
All CA Foundation notes →
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