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RRB Group D Mathematics (Arithmetic) Syllabus

The Mathematics (Arithmetic) syllabus for RRB Group D in full: 6 chapters, 24 topics and 62 sub-topics, every one listed below, plus 50 Mathematics (Arithmetic) flashcards with answers.

6Chapters
24Topics
62Sub-topics
50Flashcards

Mathematics (Arithmetic) syllabus: all 6 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number System and Basic Arithmetic

     5 topics
    • Number Systems
      • Natural, whole, integer, rational and irrational numbers
      • Place value and face value
      • Comparison and ordering of numbers
    • BODMAS and Simplification
      • Order of operations (BODMAS rule)
      • Simplification of bracketed expressions
      • Surds and indices basics
    • Divisibility and Factors
      • Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 11
      • Prime and composite numbers
      • Unit digit and remainder problems
    • LCM and HCF
      • Prime factorization and division methods
      • LCM and HCF of fractions
      • Word problems on bells, races and pipes alignment
    • Fractions and Decimals
      • Conversion between fractions and decimals
      • Operations on fractions and decimals
      • Recurring decimals

  2. Ratio, Proportion and Percentage

     4 topics
    • Ratio and Proportion
      • Simplest form and equivalent ratios
      • Direct, inverse and compound proportion
      • Dividing a quantity in a given ratio
    • Percentage
      • Conversion between percentage, fraction and ratio
      • Percentage increase and decrease
      • Successive percentage change
    • Average
      • Average of numbers and observations
      • Weighted average
      • Change in average on addition or removal of items
    • Mixture and Alligation
      • Rule of alligation
      • Mixing of two or more ingredients
      • Replacement of part of a mixture

  3. Commercial Mathematics

     3 topics
    • Profit and Loss
      • Cost price, selling price, marked price
      • Profit and loss percentage
      • Discount and successive discount
      • Dishonest dealer and false weights
    • Simple Interest
      • Principal, rate, time and amount
      • Finding any unknown quantity
    • Compound Interest
      • Annual, half-yearly and quarterly compounding
      • Difference between SI and CI
      • Growth and depreciation

  4. Time, Work, Speed and Distance

     4 topics
    • Time and Work
      • Individual and combined work rates
      • Work and wages distribution
      • Efficiency-based problems
    • Pipes and Cisterns
      • Filling and emptying pipes
      • Leak problems
    • Time, Speed and Distance
      • Conversion of units (km/h to m/s)
      • Average speed and relative speed
    • Trains, Boats and Streams
      • Train crossing pole, platform and another train
      • Upstream and downstream speed

  5. Algebra, Geometry and Mensuration

     4 topics
    • Elementary Algebra
      • Algebraic identities and factorization
      • Linear equations in one and two variables
    • Geometry Basics
      • Lines, angles and triangles
      • Circles and quadrilaterals
      • Similarity and congruence
    • Mensuration
      • Area and perimeter of 2D figures
      • Volume and surface area of cube, cuboid, cylinder, cone and sphere
    • Trigonometry Basics
      • Trigonometric ratios and standard angles
      • Heights and distances

  6. Statistics, Calendar and Clock

     4 topics
    • Elementary Statistics
      • Mean, median and mode
      • Data interpretation from tables and graphs
    • Calendar
      • Odd days and leap year concept
      • Finding day of the week
    • Clock
      • Angle between hour and minute hands
      • Coincidence and opposite positions of hands
    • Age Problems
      • Present, past and future age relations
      • Ratio-based age problems

RRB Group D Mathematics (Arithmetic) flashcards — 50 questions with answers

  1. What are natural numbers?

    The counting numbers starting from 1: 1, 2, 3, 4, ... (positive integers, excluding 0).

  2. What are whole numbers?

    All natural numbers together with 0: 0, 1, 2, 3, 4, ...

  3. What is the difference between a prime number and a composite number?

    A prime number has exactly two factors (1 and itself), e.g. 2, 3, 5, 7. A composite number has more than two factors, e.g. 4, 6, 8, 9. (1 is neither prime nor composite.)

  4. What is the only even prime number?

    2 is the only even prime number; all other even numbers are divisible by 2 and hence composite.

  5. What is the difference between rational and irrational numbers?

    A rational number can be expressed as p/q where q ≠ 0 (e.g. 1/2, 0.75). An irrational number cannot be written as a fraction; its decimal is non-terminating and non-repeating (e.g. √2, π).

  6. What is the place value vs. face value of a digit?

    Face value is the digit itself, regardless of position. Place value is the digit multiplied by its positional value. In 352, the digit 5 has face value 5 and place value 50.

  7. What does BODMAS stand for and what order does it impose?

    Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — the order of operations to simplify expressions. Division and Multiplication rank equally (left to right), as do Addition and Subtraction.

  8. In BODMAS, which is solved first in brackets: which order of brackets?

    Innermost first: ( ) round brackets, then { } curly brackets, then [ ] square brackets (vinculum/bar even before round brackets).

  9. Using BODMAS, simplify 2 + 3 × 4.

    14. Multiplication first: 3 × 4 = 12, then 2 + 12 = 14 (not 20).

  10. What is the divisibility rule for 3?

    A number is divisible by 3 if the sum of its digits is divisible by 3. E.g. 372 → 3+7+2 = 12, divisible by 3.

  11. What is the divisibility rule for 4?

    A number is divisible by 4 if the number formed by its last two digits is divisible by 4. E.g. 1316 → 16 is divisible by 4.

  12. What is the divisibility rule for 8?

    A number is divisible by 8 if the number formed by its last three digits is divisible by 8. E.g. 7128 → 128 ÷ 8 = 16.

  13. What is the divisibility rule for 9?

    A number is divisible by 9 if the sum of its digits is divisible by 9. E.g. 729 → 7+2+9 = 18, divisible by 9.

  14. What is the divisibility rule for 11?

    A number is divisible by 11 if the difference between the sum of digits in odd places and the sum of digits in even places is 0 or a multiple of 11. E.g. 4829 → (9+8) − (2+4) = 11.

  15. What is the divisibility rule for 6?

    A number is divisible by 6 if it is divisible by both 2 and 3 (i.e. it is even and its digit sum is divisible by 3).

  16. How do you find the total number of factors of a number from its prime factorization?

    If N = a^p × b^q × c^r, the number of factors = (p+1)(q+1)(r+1). E.g. 72 = 2³×3² → (3+1)(2+1) = 12 factors.

  17. What is the HCF (GCD) of two numbers?

    The Highest Common Factor is the largest number that divides both numbers exactly (the greatest common divisor).

  18. What is the LCM of two numbers?

    The Least Common Multiple is the smallest number that is exactly divisible by both numbers.

  19. What is the relationship between LCM, HCF and the two numbers?

    For two numbers a and b: LCM × HCF = a × b. So one can be found if the other three are known.

  20. How do you find the HCF and LCM of fractions?

    HCF of fractions = HCF of numerators / LCM of denominators. LCM of fractions = LCM of numerators / HCF of denominators.

Show the other 30 Mathematics (Arithmetic) flashcards

  1. What is a proper fraction vs. an improper fraction?

    A proper fraction has numerator less than denominator (e.g. 3/5). An improper fraction has numerator greater than or equal to the denominator (e.g. 7/4).

  2. How do you convert a fraction to a decimal and vice versa?

    Fraction to decimal: divide numerator by denominator. Decimal to fraction: write the decimal over the appropriate power of 10 and simplify, e.g. 0.25 = 25/100 = 1/4.

  3. How do you compare two fractions a/b and c/d quickly?

    Cross-multiply: compare a×d with c×b. If a×d > c×b then a/b > c/d (for positive denominators).

  4. What is a ratio and how is a:b interpreted?

    A ratio a:b is a comparison of two quantities of the same kind, equal to the fraction a/b. It tells how many times one quantity contains the other.

  5. What is a proportion and what is the rule of cross-products?

    A proportion states two ratios are equal: a:b = c:d (i.e. a/b = c/d). The cross-product rule gives a×d = b×c (product of extremes = product of means).

  6. In the proportion a:b = c:d, what are the means and extremes?

    a and d are the extremes; b and c are the means. The mean proportional between a and b is √(ab).

  7. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    a:b:c = 8:12:15. Make b common: a:b = 8:12 (×4), b:c = 12:15 (×3), so a:b:c = 8:12:15.

  8. How do you convert a fraction or ratio to a percentage?

    Multiply by 100 and add the % sign. E.g. 3/4 = (3/4)×100 = 75%. To convert a % to a fraction, divide by 100.

  9. How do you find x% of a value N?

    x% of N = (x/100) × N. E.g. 20% of 250 = (20/100)×250 = 50.

  10. What is the formula for percentage increase or decrease?

    Percentage change = (Change in value / Original value) × 100. Increase if positive, decrease if negative.

  11. If a number is increased by 25%, by what % must it be decreased to return to the original?

    20%. Increasing by 25% gives 1.25×; to undo, decrease = (0.25/1.25)×100 = 20%.

  12. What is the formula for the average (arithmetic mean) of a set of numbers?

    Average = (Sum of all observations) / (Number of observations).

  13. What is the average of the first n natural numbers?

    Average = (n+1)/2. (Sum = n(n+1)/2, divided by n.)

  14. If the average of n quantities changes when one is added/removed, how do you find the new value?

    New sum = old average × old count ± changes; new average = new sum / new count. Use: change in total = change in average × number of items affected.

  15. What is the average speed for a round trip at speeds x and y over the same distance?

    Average speed = 2xy/(x+y), the harmonic mean (not the simple average of x and y).

  16. What is the Rule of Alligation?

    It finds the ratio in which two ingredients at given prices/concentrations must be mixed to produce a mixture of a desired mean value: (Quantity cheaper)/(Quantity dearer) = (Dearer − Mean)/(Mean − Cheaper).

  17. In a mixture, if x litres of pure liquid is replaced by water repeatedly n times in a vessel of capacity V, what fraction of pure liquid remains?

    Remaining pure liquid = V × (1 − x/V)^n. This is the standard replacement formula.

  18. What is the formula for profit and loss in terms of CP and SP?

    Profit = SP − CP (when SP > CP); Loss = CP − SP (when CP > SP). CP = cost price, SP = selling price.

  19. How do you calculate profit % and loss %?

    Profit % = (Profit/CP) × 100; Loss % = (Loss/CP) × 100. Both are always calculated on the Cost Price.

  20. How do you find SP from CP and profit/loss percentage?

    SP = CP × (100 + Profit%)/100 for profit, or SP = CP × (100 − Loss%)/100 for loss.

  21. What is marked price (MP) and how does discount relate to it?

    MP (list price) is the price marked on an item. Discount is a reduction on MP. SP = MP × (100 − Discount%)/100; discount is always calculated on MP.

  22. If an item is sold at the same price, one at x% profit and another at x% loss, what is the overall result?

    There is always an overall loss of (x/10)² %, i.e. x²/100 %. E.g. 10% each way → 1% loss.

  23. What is the formula for Simple Interest?

    SI = (P × R × T)/100, where P = principal, R = rate % per annum, T = time in years.

  24. What is the formula for the Amount under Simple Interest?

    Amount = Principal + Simple Interest = P + (P×R×T)/100 = P(1 + RT/100).

  25. Under simple interest, in how many years does a sum double at R% per annum?

    Time to double = 100/R years (since SI must equal P, so P = P×R×T/100 → T = 100/R).

  26. What is the formula for Compound Interest (compounded annually)?

    Amount = P(1 + R/100)^T, and CI = Amount − P, where P = principal, R = rate % p.a., T = time in years.

  27. How is the compound interest formula adjusted for half-yearly compounding?

    Amount = P(1 + (R/2)/100)^(2T). The rate is halved and the number of periods is doubled. (For quarterly: R/4 and 4T.)

  28. What is the key difference between Simple Interest and Compound Interest?

    SI is calculated only on the original principal each period; CI is calculated on principal plus accumulated interest, so interest earns interest.

  29. For 2 years, what is the difference between CI and SI on the same principal and rate?

    Difference = P × (R/100)². For 2 years the CI−SI gap equals the principal times the square of the rate (as a decimal).

  30. What is the shortcut to compute CI for 2 years as an effective rate?

    Effective 2-year rate = (2R + R²/100)%. E.g. at 10% for 2 years, effective = 21%, so Amount = P × 1.21.

RRB Group D Mathematics (Arithmetic) FAQ

What is in the RRB Group D Mathematics (Arithmetic) syllabus?

RRB Group D Mathematics (Arithmetic) is split into 6 chapters: Number System and Basic Arithmetic, Ratio, Proportion and Percentage, Commercial Mathematics, Time, Work, Speed and Distance, Algebra, Geometry and Mensuration and Statistics, Calendar and Clock. Together they contain 24 topics and 62 sub-topics.

How many chapters are in RRB Group D Mathematics (Arithmetic)?

6 chapters, containing 24 topics and 62 sub-topics. The largest chapter is Number System and Basic Arithmetic, with 5 topics.

Are there flashcards for RRB Group D Mathematics (Arithmetic)?

Yes — a 50-card Mathematics (Arithmetic) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.