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RRB NTPC Mathematics (Quantitative Aptitude) Syllabus

The Mathematics (Quantitative Aptitude) syllabus for RRB NTPC in full: 5 chapters, 26 topics and 60 sub-topics, every one listed below, plus 50 Mathematics (Quantitative Aptitude) flashcards with answers.

5Chapters
26Topics
60Sub-topics
50Flashcards

Mathematics (Quantitative Aptitude) syllabus: all 5 chapters

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

  1. Number System and Arithmetic Foundations

     5 topics
    • Classification of Numbers
      • Natural, whole, integers, rational and irrational numbers
      • Even, odd, prime and composite numbers
      • Place value and face value
    • Divisibility and Factors
      • Divisibility rules for 2 to 11
      • Factors, multiples and number of divisors
      • Unit digit and cyclicity of powers
    • LCM and HCF
      • HCF and LCM by prime factorisation and division
      • Relation: product of numbers = HCF x LCM
      • LCM and HCF of fractions and word problems
    • Fractions, Decimals and Surds
      • Conversion and comparison of fractions
      • Recurring and terminating decimals
      • Simplification of surds and indices
    • BODMAS and Simplification
      • Order of operations
      • Approximation techniques

  2. Ratio, Proportion and Commercial Arithmetic

     6 topics
    • Ratio and Proportion
      • Compound, duplicate and inverse ratio
      • Dividing a quantity in a given ratio
      • Componendo and dividendo
    • Percentage
      • Percentage increase and decrease
      • Successive percentage change
      • Population, depreciation and election problems
    • Profit, Loss and Discount
      • Cost price, selling price and marked price
      • Successive discounts
      • Dishonest dealer and false weight
    • Simple and Compound Interest
      • Simple interest formula and instalments
      • Compound interest annually, half-yearly and quarterly
      • Difference between SI and CI
    • Average
      • Average of numbers and series
      • Weighted average and change in average
      • Average speed problems
    • Mixture and Alligation
      • Rule of alligation
      • Replacement of mixture

  3. Time, Work, Speed and Distance

     5 topics
    • Time and Work
      • Individual and combined efficiency
      • Pipes and cisterns
      • Work and wages
    • Time, Speed and Distance
      • Conversion of units (km/h and m/s)
      • Average and relative speed
    • Problems on Trains
      • Train crossing pole, platform and another train
      • Trains in same and opposite directions
    • Boats and Streams
      • Upstream and downstream speed
      • Average speed in still water
    • Problems on Ages
      • Present, past and future age ratios

  4. Algebra and Elementary Statistics

     5 topics
    • Algebraic Identities and Expressions
      • Standard identities and expansions
      • Factorisation
    • Linear and Quadratic Equations
      • Linear equations in one and two variables
      • Roots of quadratic equations
    • Elementary Statistics
      • Mean, median and mode
      • Range and frequency distribution
    • Data Interpretation
      • Tables and bar graphs
      • Pie charts and line graphs
    • Fundamentals of Trigonometry
      • Trigonometric ratios and standard angles
      • Heights and distances (basic)

  5. Geometry, Mensuration and Probability

     5 topics
    • Lines, Angles and Triangles
      • Properties of angles and triangles
      • Congruence and similarity
    • Circles and Quadrilaterals
      • Tangents and chords
      • Properties of quadrilaterals
    • Mensuration of 2D Figures
      • Area and perimeter of triangle, rectangle and circle
    • Mensuration of 3D Solids
      • Volume and surface area of cube, cuboid and cylinder
      • Cone, sphere and hemisphere
    • Permutation, Combination and Probability
      • Basic counting principle
      • Simple probability with coins, dice and cards

RRB NTPC Mathematics (Quantitative Aptitude) flashcards — 50 questions with answers

  1. What is a rational number?

    A number that can be expressed in the form p/q, where p and q are integers and q is not equal to 0 (e.g., 3/4, -5, 0.25).

  2. What is an irrational number? Give two examples.

    A number that cannot be expressed as p/q with integers p and q; its decimal is non-terminating and non-repeating. Examples: square root of 2, and pi.

  3. What is a prime number? Which is the only even prime number?

    A natural number greater than 1 having exactly two factors, 1 and itself. The only even prime number is 2.

  4. What are co-prime (relatively prime) numbers?

    Two numbers whose HCF (greatest common factor) is 1, e.g., 8 and 15. They need not individually be prime.

  5. Classify whole numbers, natural numbers, and integers.

    Natural numbers: 1, 2, 3, ... Whole numbers: 0, 1, 2, 3, ... (natural numbers plus 0). Integers: ..., -2, -1, 0, 1, 2, ... (positive, negative, and zero).

  6. State the divisibility rule for 3 and for 9.

    Divisible by 3 if the sum of digits is divisible by 3. Divisible by 9 if the sum of digits is divisible by 9.

  7. State the divisibility rule for 4 and for 8.

    Divisible by 4 if the number formed by the last two digits is divisible by 4. Divisible by 8 if the number formed by the last three digits is divisible by 8.

  8. State the divisibility rule for 11.

    A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

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

    If N = a^p × b^q × c^r (prime factorization), the number of factors = (p+1)(q+1)(r+1).

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

    Product of two numbers = HCF × LCM. So HCF × LCM = first number × second number.

  11. What is the HCF (Highest Common Factor) of two or more numbers?

    The largest number that divides each of the given numbers exactly (without remainder).

  12. What is the LCM (Least Common Multiple) of two or more numbers?

    The smallest number that is exactly divisible by each of the given numbers.

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

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

  14. What is the smallest number which when divided by a, b, c leaves the same remainder r in each case?

    It is (LCM of a, b, c) + r.

  15. What is a surd? Give an example.

    An irrational root of a rational number that cannot be simplified to remove the root, e.g., square root of 2 or cube root of 5.

  16. How do you rationalize the denominator of 1/(a + sqrt(b))?

    Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b)) / (a^2 - b).

  17. What does BODMAS stand for?

    Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — the order of operations in simplification.

  18. In BODMAS, what is the order for solving brackets?

    Solve brackets in order: first ( ), then { }, then [ ] — innermost brackets are solved first.

  19. How do you convert a fraction to a decimal and a decimal to a percentage?

    Fraction to decimal: divide numerator by denominator. Decimal to percentage: multiply by 100 and add the % sign.

  20. What is the definition of a ratio?

    A ratio is a comparison of two quantities of the same kind by division, written as a:b or a/b, where b is not 0.

Show the other 30 Mathematics (Quantitative Aptitude) flashcards

  1. What is proportion? State the rule of cross-multiplication.

    Proportion is the equality of two ratios: a:b = c:d. Then a×d = b×c (product of extremes = product of means).

  2. What is the mean proportional between two numbers a and b?

    The mean proportional (geometric mean) is the square root of (a × b).

  3. If a:b = 2:3 and b:c = 4:5, find a:b:c.

    Make b common: a:b = 8:12, b:c = 12:15, so a:b:c = 8:12:15.

  4. What is the formula for percentage of a value?

    Percentage value = (Required quantity / Total quantity) × 100. To find x% of N, compute (x/100) × N.

  5. If a number is increased by x% and then decreased by x%, what is the net change?

    There is a net decrease of (x^2/100)%, regardless of the original number.

  6. How do you convert the fraction 1/8 to a percentage?

    1/8 = 0.125 = 12.5%.

  7. How is profit or loss percentage calculated?

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

  8. Define Cost Price (CP), Selling Price (SP), and Marked Price (MP).

    CP: price at which an article is bought. SP: price at which it is sold. MP: the labelled/list price before discount.

  9. What is the formula relating SP and CP using profit%?

    SP = CP × (100 + Profit%) / 100. For a loss: SP = CP × (100 - Loss%) / 100.

  10. How is discount calculated?

    Discount is given on the Marked Price. Discount% = (Discount / Marked Price) × 100, and SP = MP - Discount.

  11. If two articles are sold at the same SP, one at x% profit and the other at x% loss, what is the overall result?

    There is always an overall loss of (x^2/100)%.

  12. What is the formula for Simple Interest (SI)?

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

  13. What is the formula for the Amount in Simple Interest?

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

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

    Amount = P × (1 + R/100)^T, and Compound Interest = Amount - P, where T is the number of years.

  15. How is compound interest amount calculated when compounded half-yearly?

    Amount = P × (1 + (R/2)/100)^(2T): the rate is halved and the time period is doubled.

  16. For the same P, R, and T, how do SI and CI compare?

    CI is always greater than SI (for T greater than 1 year) because CI earns interest on accumulated interest; they are equal for the first year.

  17. What is the difference between CI and SI for 2 years?

    Difference = P × (R/100)^2, where P is principal and R is rate per annum.

  18. What is the formula for average?

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

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

    Average = (n + 1) / 2.

  20. If the average of n numbers is A, and a new number is added making the count n+1 with the average unchanged, what is the new number?

    The new number must equal A (the average itself), since adding the average keeps the average the same.

  21. What is the formula for the average speed for equal distances at speeds x and y?

    Average speed = 2xy / (x + y), the harmonic mean of the two speeds.

  22. What is alligation, and what does the rule of alligation find?

    Alligation is a method to find the ratio in which two ingredients at different prices/concentrations must be mixed to get a mixture at a given mean price/concentration.

  23. State the rule of alligation formula.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper).

  24. A container has milk and water. If x liters of milk is removed and replaced with water n times, what fraction of milk remains?

    Remaining milk = Initial quantity × (1 - x/Total)^n.

  25. In Time and Work, if A can do a job in n days, what is A's one-day work?

    A's one day's work = 1/n of the total work.

  26. If A does a job in x days and B in y days, how long do they take working together?

    Together they take xy/(x + y) days, since combined one-day work = 1/x + 1/y.

  27. What is the relationship between efficiency and time taken to complete work?

    Efficiency is inversely proportional to time. If A is twice as efficient as B, A takes half the time B takes. Ratio of efficiencies = inverse ratio of times.

  28. State the work equivalence formula (M1 D1 / W1 = M2 D2 / W2).

    (M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2, where M = men, D = days, H = hours/day, W = work. Used in chain rule problems.

  29. If A and B together finish a work in T days and A alone in a days, how long does B alone take?

    B's time = (a × T) / (a - T) days, derived from 1/B = 1/T - 1/a.

  30. What is the percentage equivalent of the fractions 1/4, 1/3, and 2/3?

    1/4 = 25%, 1/3 = 33.33%, 2/3 = 66.67%.

RRB NTPC Mathematics (Quantitative Aptitude) FAQ

What is in the RRB NTPC Mathematics (Quantitative Aptitude) syllabus?

RRB NTPC Mathematics (Quantitative Aptitude) is split into 5 chapters: Number System and Arithmetic Foundations, Ratio, Proportion and Commercial Arithmetic, Time, Work, Speed and Distance, Algebra and Elementary Statistics and Geometry, Mensuration and Probability. Together they contain 26 topics and 60 sub-topics.

How many chapters are in RRB NTPC Mathematics (Quantitative Aptitude)?

5 chapters, containing 26 topics and 60 sub-topics. The largest chapter is Ratio, Proportion and Commercial Arithmetic, with 6 topics.

Are there flashcards for RRB NTPC Mathematics (Quantitative Aptitude)?

Yes — a 50-card Mathematics (Quantitative Aptitude) 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.