CA Foundation Quantitative Aptitude Chapter by Chapter: Weightage and Worked Examples

Paper 3 rewards students who can recognise a question type in ten seconds and know the shortest route to the answer. This guide goes chapter by chapter through ICAI's syllabus, gives the official weightage for each section, and works one representative question from each high-value area. For the exam pattern and a week-by-week plan, see our Quantitative Aptitude preparation guide.

The Weightage in One View

ICAI's section-wise weightage was issued on 26 October 2023 and applies from May 2024 until ICAI changes it. Each section may deviate by up to plus or minus 5%. The percentages below are shares of each part's marks.

Part A, Business Mathematics (40 marks): Section I, chapters 1 to 3 (ratio, indices, logarithms, equations, linear inequalities): 20% to 30%. Section II, chapter 4 (mathematics of finance): 30% to 40%. Section III, chapters 5 to 8 (permutations and combinations, sequences and series, sets, relations, functions, limits, calculus): 30% to 50%.
Part B, Logical Reasoning (20 marks): chapters 9 to 12, each 20% to 30%.
Part C, Statistics (40 marks): chapters 13 and 14 (data, sampling, central tendency and dispersion): 45% to 50%. Chapters 15 and 16 (probability, theoretical distributions): 25% to 30%. Chapter 17 (correlation and regression): 10% to 15%. Chapter 18 (index numbers): 10% to 15%.

In marks, mathematics of finance is worth about 12 to 16 and chapters 13 and 14 together about 18 to 20. Those two blocks alone make up roughly a third of the paper.

Business Mathematics

Chapter 1: Ratio and Proportion, Indices and Logarithms

Ratio. If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c. Make b equal in both ratios by multiplying the first by 4 and the second by 3. That gives a : b = 8 : 12 and b : c = 12 : 15, so a : b : c = 8 : 12 : 15.

Indices. If 3ⁿ⁺¹ + 3^n-1 = 270, find n. Take out 3^n-1: 3^n-1(9 + 1) = 270, so 3^n-1 = 27 = 3³ and n = 4.

Logarithms. Given log 2 = 0.3010 and log 3 = 0.4771, find log 12. log 12 = log (2² x 3) = 2(0.3010) + 0.4771 = 1.0791. Most log questions work the same way: break the number into prime factors and apply the three laws.

Practise: Chapter 1 MCQs.

Chapters 2 and 3: Equations and Linear Inequalities

For quadratic MCQs, use the sum of roots (-b/a) and the product of roots (c/a) instead of solving. For x² - 2x - 35 = 0 the roots are 7 and -5, with sum 2 and product -35. For inequalities, test a point such as (0, 0) against each inequality to see which side of the line is feasible. Practise: Equations, Linear Inequalities.

Chapter 4: Mathematics of Finance

This is the largest single section. Learn the formulas until you can write them without thinking, and practise with your calculator's memory keys.

Effective rate. 12% p.a. compounded quarterly: (1 + 0.03)⁴ - 1 = 1.1255 - 1 = 12.55%.

Present value of an annuity. ₹10,000 received at the end of each year for 3 years at 10%: PV = 10,000 x [1 - (1.10)^-3] / 0.10 = 10,000 x 2.4869 = ₹24,869 (approximately).

EMI. A loan of ₹1,00,000 at 12% p.a., repaid monthly over 12 months. Monthly rate i = 1% and n = 12. EMI = P x i x (1 + i)ⁿ / [(1 + i)ⁿ - 1] = 1,00,000 x 0.01 x 1.1268 / 0.1268 = ₹8,885 (approximately).

CAGR. An investment grows from ₹50,000 to ₹72,000 in 4 years. CAGR = (72,000 / 50,000)^1/4 - 1 = (1.44)^0.25 - 1 = 9.54%. On an ordinary calculator, press the square-root key twice to take a fourth root.

Check your workings with our compound interest calculator and loan amortisation calculator, then practise: Chapter 4 MCQs.

Chapters 5 to 8: Permutations, Series, Sets and Calculus

Combinations: a committee of 3 chosen from 7 people is ⁷C₃ = 35. Six people seated round a table can be arranged in (6 - 1)! = 120 ways.
Arithmetic progression: the sum of the first 20 terms of 3, 7, 11, ... is S = n/2 [2a + (n - 1)d] = 10 x [6 + 76] = 820.
Calculus: if total cost C = 2x² + 5x + 100, marginal cost = dC/dx = 4x + 5, which is 45 at x = 10.

Section III can carry up to half of Business Mathematics, so skipping calculus is expensive. Practise: Permutations and Combinations, Sequence and Series, Sets, Relations, Functions and Limits, Calculus.

Logical Reasoning

Direction test. Ravi walks 5 km north, turns right and walks 3 km, then turns right again and walks 9 km. Where is he? Plot it: after the first two legs he is at (3, 5), and walking 9 km south takes him to (3, -4). His distance from the start is the square root of (3² + 4²) = 5 km, to the south-east.

Draw every direction and seating question rather than holding it in your head. Twenty questions a day for a month makes this section close to risk-free. Practise: Number Series and Coding, Direction Tests, Seating Arrangements, Blood Relations.

Statistics

Chapters 13 and 14: Data, Sampling, Central Tendency and Dispersion

For the data 2, 4, 4, 4, 5, 5, 7, 9: mean = 40 / 8 = 5. The squared deviations are 9, 1, 1, 1, 0, 0, 4 and 16, totalling 32. Variance = 32 / 8 = 4, so SD = 2 and the coefficient of variation = 2 / 5 x 100 = 40%. Also learn the effect of a change of origin and scale: adding a constant changes the mean but not the SD, and multiplying by k multiplies the SD by |k|. Practise: Chapter 13, Chapter 14.

Chapters 15 and 16: Probability and Theoretical Distributions

Two dice are thrown. P(sum = 8): the favourable outcomes are (2,6), (3,5), (4,4), (5,3) and (6,2), so the probability is 5/36. For a binomial distribution with n = 10 and p = 0.4: mean = np = 4 and variance = npq = 10 x 0.4 x 0.6 = 2.4. A common trap: the variance of a binomial distribution is always less than its mean. Practise: Probability, Theoretical Distributions.

Chapters 17 and 18: Correlation, Regression and Index Numbers

If b_xy = 0.4 and b_yx = 0.9, then r = the square root of (0.4 x 0.9) = 0.6, taking the common sign of the two coefficients. For a Laspeyres price index with item A (p₀ 10, q₀ 5, p₁ 12) and item B (p₀ 20, q₀ 2, p₁ 25), the index is (sum of p₁q₀) / (sum of p₀q₀) x 100 = 110 / 90 x 100 = 122.22. Practise: Correlation and Regression, Index Numbers.

How to Use the Examples

Solve before you look at the options. The distractors are built from the usual slips, such as using the nominal rate instead of the effective rate, or n instead of n - 1.
Keep an error log by chapter. If three of your last ten errors are in mathematics of finance, your next session goes there.
Mind the penalty. A wrong answer costs 0.25 marks, so a careless error on a question you could solve costs 1.25 marks compared with getting it right.

Start with the full CA Foundation QA MCQ bank, then move to timed tests on the QA practice page.

FAQs

Which QA chapter carries the most marks?
Mathematics of finance, at 30% to 40% of Business Mathematics (about 12 to 16 marks). In Statistics, chapters 13 and 14 together carry 45% to 50% of the 40 marks.

Can I skip calculus in CA Foundation?
It sits in Section III, which ICAI weights at 30% to 50% of Business Mathematics together with permutations, series and sets. Skipping it puts several marks at risk.

Is a scientific calculator allowed?
No. ICAI's guidance notes (the Foundation notes for June 2024 and the Intermediate notes for September 2026, for example) allow a battery-operated calculator with up to 6 functions, 12 digits and two memories, and say scientific calculators are not allowed. Check the Foundation guidance note for your attempt in ICAI's examination announcements.

Are these worked examples from ICAI papers?
No. They are original examples written to match the question types in ICAI's papers. Use ICAI's RTPs, MTPs and past papers for actual exam questions.

Sources

ICAI BoS, Foundation syllabus with section-wise weightage (issued 26 October 2023, applicable from May 2024).
ICAI, FAQs on the New Scheme of Education and Training: 0.25-mark negative marking in objective papers.
ICAI, Foundation May 2026 Paper 3 question paper: 100 compulsory questions in 2 hours.
ICAI, Foundation June 2024 guidance notes and Intermediate September 2026 guidance notes: calculator rules.
ICAI BoS, BoS Knowledge Portal: study material, RTPs and MTPs for Paper 3.