RRB RPF Constable Mathematics Syllabus

The Arithmetic section of the RRB RPF Constable CBT 2027 carries 35 questions and 35 marks out of a total of 120 questions and 120 marks in 90 minutes. It is tested at the Class 10 (Matriculation) level, consistent with the minimum educational qualification for the RPF Constable post. Questions test numerical ability, arithmetic reasoning, and calculation accuracy rather than advanced mathematical theory. The section rewards candidates who combine conceptual clarity with calculation speed and shortcut techniques.

Quick Facts: RPF Constable Arithmetic

Detailed Arithmetic Syllabus

All topics listed below are tested at Class 10 level. Questions are typically single-step or two-step numerical problems. Priority should be given to topics marked Very High in the weightage table.

1. Number System

•        Natural numbers, whole numbers, integers, rational and irrational numbers, real numbers -- definitions and examples

•        Divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 -- with examples and applications

•        HCF (Highest Common Factor): prime factorisation method; division method (Euclid's Algorithm); HCF of three or more numbers

•        LCM (Lowest Common Multiple): prime factorisation method; relationship LCM x HCF = product of two numbers

•        Applications of HCF and LCM: tiling problems; minimum capacity containers; rope cutting; bell ringing problems

•        Simplification: BODMAS rule; complex arithmetic expressions with fractions, decimals, and brackets

•        Fractions and Decimals: operations; conversion; comparison; recurring decimals

2. Percentage

•        Percentage as parts per hundred; converting fraction and ratio to percentage

•        Percentage of a quantity; finding original value when percentage is given

•        Percentage increase and decrease; net change after successive percentage changes

•        Population-based problems (growth and decline using percentage)

•        Percentage applied to income, expenditure, and savings problems

3. Ratio and Proportion

•        Simple ratio; equivalent ratios; compound ratio; inverse ratio

•        Direct proportion and inverse proportion: identification and calculation

•        Mean proportion and third proportional

•        Partnership problems: simple partnership (investment x time); compound partnership

•        Ratio in mixtures and alloys: initial and final ratio problems

4. Profit, Loss and Discount

•        Cost Price (CP), Selling Price (SP), Marked Price (MP), Trade Discount -- definitions and relationships

•        Profit percentage = (SP-CP)/CP x 100; Loss percentage = (CP-SP)/CP x 100

•        Finding CP when SP and profit/loss% are given

•        Discount on Marked Price; successive discounts; equivalent single discount formula: D = d1 + d2 - (d1 x d2)/100

•        Dishonest dealer problems: using faulty weights; selling at CP but with false weight

•        Selling at successive profit then loss; net profit or loss calculation

5. Simple Interest and Compound Interest

•        SI = (P x R x T) / 100; finding P, R, or T when SI is given

•        Amount = P + SI; Amount = P(1 + R/100)^T for CI

•        CI compounded annually, half-yearly, quarterly -- applying modified rate

•        Difference between CI and SI for 2 years = P(R/100)^2

•        Difference between CI and SI for 3 years = P(R/100)^2 x (3 + R/100)

•        Instalment problems: finding instalment when total CI amount is given

6. Time and Work

•        Work done in D days; fraction of work done per day; days required to complete a fraction

•        Combined work: if A does in a days and B in b days, together = ab/(a+b) days

•        Work done by A, B, and C together; finding individual days from combined info

•        Negative work: one person builds while another demolishes

•        Pipes and Cisterns: filling rate; emptying rate; combined rate when both pipes open; time for partial fill/empty

7. Time, Speed and Distance

•        Distance = Speed x Time; unit conversion: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h

•        Average speed = Total Distance / Total Time (NOT average of speeds)

•        Relative speed: same direction = difference of speeds; opposite direction = sum of speeds

•        Trains: length of train + length of platform = distance covered when crossing; two train crossing

•        Boats and Streams: downstream speed = boat speed + stream speed; upstream speed = boat speed - stream speed; speed of boat in still water = (D+U)/2; speed of stream = (D-U)/2

8. Mixture and Alligation

•        Alligation rule: (Quantity of cheaper) / (Quantity of dearer) = (dearer price - mean price) / (mean price - cheaper price)

•        Alligation cross diagram method -- step-by-step

•        Mixture problems: mixing two solutions of different concentrations; finding resultant concentration

•        Removing and replacing: if x litres is removed from a vessel and replaced with another liquid repeatedly

9. Mensuration

•        2D Shapes: square (side a; area = a^2; perimeter = 4a); rectangle (area = l x b; perimeter = 2(l+b); diagonal = sqrt(l^2+b^2))

•        Triangle: area = (1/2) x base x height; Heron's formula; equilateral triangle area = (sqrt3/4)a^2

•        Parallelogram: area = base x height; rhombus: area = (1/2) x d1 x d2; trapezium: area = (1/2)(a+b) x h

•        Circle: area = pi r^2; circumference = 2pi r; area of sector = (theta/360) x pi r^2; arc length = (theta/360) x 2pi r; area of segment = sector - triangle area

•        3D Shapes: cube (TSA = 6a^2; volume = a^3); cuboid (TSA = 2(lb+bh+hl); volume = l x b x h)

•        Cylinder: CSA = 2pi r h; TSA = 2pi r(r+h); volume = pi r^2 h

•        Cone: CSA = pi r l (l = slant height = sqrt(r^2+h^2)); TSA = pi r(r+l); volume = (1/3)pi r^2 h

•        Sphere: TSA = 4pi r^2; volume = (4/3)pi r^3; hemisphere: CSA = 2pi r^2; TSA = 3pi r^2; volume = (2/3)pi r^3

•        Frustum: CSA = pi(R+r)l; TSA = pi(R^2 + r^2 + (R+r)l); volume = (pi h/3)(R^2 + Rr + r^2)

10. Elementary Algebra

•        Algebraic identities: (a+b)^2 = a^2+2ab+b^2; (a-b)^2 = a^2-2ab+b^2; (a+b)(a-b) = a^2-b^2; (a+b)^3; (a-b)^3; a^3+b^3; a^3-b^3

•        Linear equations in one variable: forming and solving word problems

•        Linear equations in two variables: substitution method; elimination method; cross-multiplication; word problems

•        Quadratic equations: factorisation method; quadratic formula x = (-b +/- sqrt(b^2-4ac)) / 2a; nature of roots (D = b^2-4ac)

11. Geometry

•        Lines and Angles: supplementary; complementary; vertically opposite angles; alternate interior; corresponding; co-interior angles with parallel lines and transversals

•        Triangle Properties: angle sum = 180 degrees; exterior angle theorem; Pythagoras theorem and converse; Pythagorean triplets (3-4-5; 5-12-13; 8-15-17; 7-24-25)

•        Congruence: SSS; SAS; ASA; AAS; RHS

•        Similarity: AA; SSS; SAS; Basic Proportionality Theorem (BPT / Thales theorem); ratio of areas = square of ratio of corresponding sides

•        Circle Theorems: angle in a semicircle = 90 degrees; angle subtended by arc at centre = 2 x angle at circumference; equal chords subtend equal angles; tangent perpendicular to radius at point of tangency; tangent-secant relationship

12. Trigonometry

•        sin, cos, tan, cosec, sec, cot -- definitions using right triangle; reciprocal relationships

•        Trigonometric values at 0, 30, 45, 60, 90 degrees -- complete table

•        Fundamental identities: sin^2 theta + cos^2 theta = 1; 1 + tan^2 theta = sec^2 theta; 1 + cot^2 theta = cosec^2 theta

•        Complementary angle relationships: sin(90-theta) = cos theta; tan(90-theta) = cot theta; etc.

•        Heights and Distances: angle of elevation; angle of depression; problems with single angle

13. Statistics

•        Arithmetic Mean: direct method; assumed mean method; step deviation method for grouped data

•        Median: for ungrouped data (arrange and pick middle); for grouped data (median class; formula)

•        Mode: for ungrouped data (most frequent); for grouped data (modal class; formula)

•        Graphical Representation: reading and interpreting bar graphs; pie charts (converting marks to angles); histograms; frequency polygons

Topic-wise Weightage

Preparation Tips

1. Master the Arithmetic Cluster First

Over 35 to 40% of Arithmetic questions come from the arithmetic cluster: Percentage, Profit and Loss, SI and CI, Ratio and Proportion, Time and Work, and TSD. Master these topics first before moving to Mensuration, Algebra, and Geometry.

2. Learn Shortcuts and Mental Calculation Tricks

Speed is critical with 35 questions in approximately 26 to 28 minutes. Learn fraction-to-percentage conversions (1/8 = 12.5%, 1/6 = 16.67%, 3/8 = 37.5%), multiplication tricks, percentage shortcuts, and approximation methods to reduce calculation time.

3. Practise Daily Under Timed Conditions

Solve at least 30 to 40 Arithmetic questions daily under timed conditions. Use previous years' RPF Constable and SSC GD level Arithmetic papers for calibrated difficulty practice.

Frequently Asked Questions

Q1. Is a calculator allowed in the RPF Constable CBT?

No. Calculators are not permitted. All calculations must be performed mentally or on the rough paper provided at the exam centre.

Q2. What is the exact difficulty level of RPF Constable Arithmetic?

The difficulty is at Class 10 (Matriculation) level. Questions are typically single or two-step, testing standard formulae and direct applications rather than complex multi-step problems.