Which Quantitative Aptitude topics matter most for UPSC CAPF (AC)?

carry the highest question counts based on previous-year analyses.

Is this Quantitative Aptitude material free?

Yes — every chapter, practice set and flashcard deck here is free. Premium mock tests and live courses from tutors are labelled separately.

UPSC CAPF (AC)Quantitative Aptitude

Quantitative Aptitude for UPSC CAPF (AC)

A smaller slice of Paper I, sharing SSC CGL's full quant syllabus.

📊 ~15–20 Q of Paper I's 125

How toppers play this section

Quant carries less weight in CAPF than in SSC CGL itself, but the underlying syllabus — arithmetic, algebra, geometry, mensuration, trigonometry, data interpretation — is identical, so full SSC CGL quant prep transfers directly. Prioritise arithmetic (percentage, profit-loss, time-speed-distance) and data interpretation first, since those question types recur most often within CAPF's smaller quant allocation.

Chapters

Built to the UPSC CAPF (AC) blueprint — notes, shortcuts, solved PYQ-style examples and practice in every chapter.

1Number System1–2 questions in Tier 1 and 2–3 in Tier 2, and the mental machinery behind half the quant paper. Divisibility rules, factor counting, HCF–LCM identities and remainder cycles — four toolkits that turn "big ugly number" questions into 30-second wins.⏱ 22 min read

2Simplification, Surds and Indices2–3 quick marks per tier that reward order-of-operations discipline (VBODMAS), the index laws, and a handful of surd tricks — rationalising, nested radicals, and the a³±b³ identities. These are the fastest correct answers in the paper if you never break the operation hierarchy.⏱ 20 min read

3PercentageThe operating system of SSC arithmetic — profit & loss, interest, DI and data sufficiency all run on percentages. Master the fraction–percentage toolkit, successive change, and the multiplying-factor method, and half the quant section starts solving itself in one line.⏱ 24 min read

4Ratio and Proportion1–2 direct questions per tier — plus the language half the quant paper is written in. Chaining ratios, proportionals, coin and age templates, and componendo–dividendo, the identity that collapses three lines of algebra into one.⏱ 20 min read

5Averages1–2 questions per tier built from one identity — sum = average × count. Every "new person joins", "one is replaced", "wrong value corrected" and "average increases by" problem is that identity read in reverse. Master the change-in-average shortcut and most questions collapse to a single line.⏱ 18 min read

6Profit, Loss & Discount2–3 questions in Tier 1 and 3–4 in Tier 2 — percentage applied to buying and selling. Master the multiplying-factor chain CP → SP → MP, successive discounts, the false-weight formula and the two-item trap, and every question reduces to one line of fractions.⏱ 22 min read

7Simple and Compound Interest2–3 questions per tier built from a handful of identities — SI's straight line, CI's successive percentages, the CI−SI difference formulas, and doubling logic. Compounding is just the percentage chapter applied twice; multipliers do all the arithmetic.⏱ 20 min read

8Mixture and Alligation1–2 questions per tier decided by two tools — the alligation cross for any two-ingredient blend, and the replacement formula (V−x over V, all raised to n) for repeated draw-and-refill. Alligation is really "weighted average in reverse", so it also cracks average, speed and profit mixes.⏱ 18 min read

9Time and Work1–2 questions in Tier 1 and 2–3 in Tier 2, including pipes and cisterns. One idea — assume the total work is the LCM of the given days — converts every fraction-heavy problem into small-integer arithmetic you can do in your head.⏱ 20 min read

10Time, Speed and Distance2–3 questions per tier spanning trains, boats and chases. Four tools do all the work — the 5/18 conversion, harmonic average speed, relative speed, and the ratio trick for late/early problems. The classic error isn't hard math; it's forgetting the train's own length.⏱ 20 min read

11Partnership1 question most tiers, built on a single principle — profit is shared in proportion to capital × time (the "capital-months"). Get the capital-months ratio right, handle a working partner's commission separately, and split mid-year withdrawals into segments, and every partnership question falls out.⏱ 15 min read

12Algebra — Identities, Surds & EquationsSSC algebra is a closed game of ten identities — x + 1/x chains, a³ + b³ + c³ − 3abc, and componendo-dividendo. 2–3 questions in Tier 1, 3–5 in Tier 2, and every one of them is a known identity wearing new numbers. Learn the identity families and the substitution shortcut that cracks the rest.⏱ 26 min read

13Geometry — Triangles, Circles & QuadrilateralsThe single highest-weightage topic in SSC CGL maths — 2–4 questions in Tier 1 and 4–6 in Tier 2, built almost entirely on triangle centres, similarity, circle theorems and tangents. SSC recycles the same twenty results year after year; this chapter is those twenty results, weaponised.⏱ 30 min read

14Coordinate Geometry1–2 questions per tier from a small formula set — distance, midpoint, section, centroid, the shoelace area, and slope with its parallel/perpendicular rules. Every question is "plug the points into the right formula", so speed comes from knowing which formula the wording is pointing at.⏱ 16 min read

15Mensuration — 2D & 3D2–3 questions in Tier 1 and 3–4 in Tier 2 — areas, volumes and surface areas of the standard solids, plus SSC's favourite composites: melting and recasting, wire-drawing, rolling a sheet into a cylinder, and the cone-hemisphere-cylinder family on equal bases.⏱ 24 min read

16Trigonometry — Ratios & Identities2–3 questions in Tier 1 and 3–4 in Tier 2 — identity manipulation, standard-angle values and complementary-angle collapses. SSC trigonometry never needs a calculator: every question is one of six identity moves or a value substitution. Heights & distances gets its own chapter.⏱ 24 min read

17Heights and Distances1 question most tiers, all built on tan θ = height ÷ base and the three standard angles (30°, 45°, 60°). Draw the right triangle, place the angle, and read off the side. The two-angle "walks toward the tower" problem is the one worth drilling until it's automatic.⏱ 15 min read

18Data InterpretationSSC's guaranteed question block — a 3–5 question set on a table, bar graph, pie chart or histogram in every paper. DI is not a topic, it's applied percentage and ratio at reading speed. Learn the four chart types, the five question patterns, and the approximation discipline that makes the set a 4-minute sweep.⏱ 22 min read

19Statistics and ProbabilityA Tier-2 add-on worth 2–4 marks — mean/median/mode and their empirical link, plus basic probability on coins, dice and a 52-card deck. All of it is counting: probability is favourable ÷ total, and the central-tendency measures are three ways of summarising a list. Learn the card and dice facts cold.⏱ 18 min read

Topic-wise weightage in UPSC CAPF (AC)

Expected question counts from previous-year paper analyses. Topics with an arrow already have a full chapter.

Topic	Paper I Q	Priority
Number System & Simplification	1–2	Medium
Percentage	1–2	High
Profit, Loss & Discount	1–2	High
Simple & Compound Interest	1–2	Medium
Ratio & Proportion	1	Medium
Partnership	0–1	Low
Average	1	Medium
Time, Speed & Distance	1–2	High
Time & Work	1–2	High
Algebra	1–2	Medium
Geometry	1–2	Medium
Mensuration	1	Low
Trigonometry	1	Low
Data Interpretation	2–3	High