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RRB NTPC Mathematics Practice Test Online

Build a faster, more reliable approach to Number System, Arithmetic, Algebra and Mensuration for RRB NTPC and related Railway exams.

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Reviewed by Anna Nagaraj · Assistant Audit Officer, DG Audit (Railways), Secunderabad · Cleared SSC CGL with All India Rank 442.Arithmetic shortcuts, algebra fundamentals, and time-saving calculation steps checked against the actual RRB NTPC CBT 1/CBT 2 format.

Last reviewed: August 2026

Exam strategy & syllabus overview

RRB NTPC Mathematics carries 30 marks in CBT 1 and 35 in CBT 2, spread across Number System, Arithmetic, Simple and Compound Interest, Time-Work-Pipes, Time-Speed-Distance, Algebra, Geometry, Mensuration, Trigonometry, and Statistics, roughly in that order of frequency. Each wrong answer costs one-third of a mark, so guessing on a Number System or profit-loss question you haven't actually worked out usually costs more than it gains.

A common mistake in the Arithmetic section is applying successive percentage changes by adding them instead of multiplying them stage by stage, which quietly produces a wrong final answer even when every individual step looked correct. Since almost none of the syllabus goes beyond Class 10 level, the section mostly separates candidates by calculation speed and by whether they check units (km/h versus m/s, for instance) before submitting an answer. This practice test also suits RRB Group D, RRB ALP, and SSC MTS aspirants preparing the same Mathematics topics.

⚡ Quick quiz

Test yourself in under a minute: RRB NTPC Mathematics Practice Test

These questions cover Number System, Interest and Speed-Distance topics to test whether you can solve NTPC-level arithmetic correctly under a real exam clock, not just eventually.

  1. 1. Find the LCM of 36 and 84.

  2. 2. Find the simple interest on Rs. 8000 at 9% per annum for 3 years.

  3. 3. A car covers a distance of 250 km in 5 hours. What is its speed in m/s?

  4. 4. The sides of a triangle are 7 cm, 24 cm, and 25 cm. Find its area.

  5. 5. Find the value of sin 60° × cos 30° + sin 30° × cos 60°.

⏱ Cutoff & exam pattern

Target Score: 24-27+ out of 30 in CBT 1 (within 15-18 minutes)

Can you solve a time-work or speed-distance problem in under a minute without reaching for a formula sheet?

CBT 1 pattern

30 Qs / 30 Marks (+1 / -0.33 penalty)

CBT 2 pattern

35 Qs / 35 Marks (+1 / -0.33 penalty)

Number System & Arithmetic

8-10 Qs

Interest, Work & Speed-Distance

8-10 Qs

Geometry, Mensuration & Trigonometry

6-8 Qs

Algebra & Statistics

4-6 Qs

CBT 1 Overall Cut-off (UR/General)

68-78 out of 100

Target Sectional Score (Maths)

23+ in CBT 1, 28+ in CBT 2

Time yourself on this set the way you would in the actual exam — accuracy under a clock is the real skill being tested here.

Number System & Arithmetic

LCM/HCF, fraction simplification, surds, percentage, profit-loss, and ratio problems.

📋 Quick referenceNumber System & Arithmetic Quick Reference▶
  • Product of two numbers = HCF x LCM.
  • SP = CP x (1 + profit%/100), or CP x (1 - loss%/100); successive percentage changes multiply, they don't add.

Speed Over New Tricks

For Aspirants

  • Number system and arithmetic questions rarely test anything beyond Class 10 material; the real gain is speed, not new tricks.
  • Practice LCM/HCF, fraction simplification, and percentage conversions with a strict 60-90 second timer per question.

  1. 1. What is the value of (2/3 + 3/4) ÷ (5/6 − 1/4)?

    ▶Reveal answer
    17/7 (2 3/7)

    Using LCM 12: 2/3 + 3/4 = 8/12 + 9/12 = 17/12, and 5/6 − 1/4 = 10/12 − 3/12 = 7/12. Dividing gives (17/12) ÷ (7/12) = 17/7.

  2. 2. Simplify: √50 + √18 − √8.

    ▶Reveal answer
    6√2

    Break each surd into a perfect-square factor: √50 = 5√2, √18 = 3√2, √8 = 2√2. Combining like surds: 5√2 + 3√2 − 2√2 = 6√2.

  3. 3. In an exam, a student scored 432 marks out of 600. What percentage of marks did the student score?

    ▶Reveal answer
    72%

    Percentage = (432/600) × 100. Simplifying 432/600 to 18/25 and multiplying by 100 gives 72%.

  4. 4. A shopkeeper bought an article for Rs. 750 and sold it for Rs. 900. Find his profit percentage.

    ▶Reveal answer
    20%

    Profit = SP − CP = 900 − 750 = Rs. 150. Profit percentage = (150/750) × 100 = 20%.

  5. 5. The ratio of ages of A and B is 4:5. If the sum of their ages is 54 years, find B's age.

    ▶Reveal answer
    30 years

    Total parts = 4 + 5 = 9, so one part = 54/9 = 6. B's age = 5 parts = 5 × 6 = 30 years.

Interest, Time-Work & Pipes

Simple and compound interest calculations, followed by an efficiency-based work problem and pipes-and-cisterns.

📋 Quick referenceInterest, Work & Pipes Quick Reference▶
  • Simple Interest = P x R x T / 100; Compound Interest = P x (1 + R/100)^T - P.
  • Combined work rate = 1/(time A) + 1/(time B); an emptying pipe subtracts its rate.

Memorize the Formula, Separate the Rates

For Aspirants

  • Memorize the two or three standard SI/CI formulas cold instead of re-deriving them each time.
  • Write out each person's or object's individual work rate separately before combining them; combining rates in your head is where most errors creep in.

  1. 1. Find the compound interest on Rs. 5000 at 10% per annum for 2 years, compounded annually.

    ▶Reveal answer
    Rs. 1050

    Amount after year 1 = 5000 × 1.1 = 5500; after year 2 = 5500 × 1.1 = 6050. CI = 6050 − 5000 = Rs. 1050.

  2. 2. A can complete a piece of work in 12 days and B can complete the same work in 18 days. In how many days will they complete the work together?

    ▶Reveal answer
    36/5 = 7.2 days

    Combined one-day work = 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time taken together = 36/5 = 7.2 days.

  3. 3. Pipe A can fill a tank in 15 hours and pipe B can empty it in 25 hours. If both pipes are opened together, how long will it take to fill the empty tank?

    ▶Reveal answer
    37.5 hours

    Net filling rate = 1/15 − 1/25 = 5/75 − 3/75 = 2/75 of the tank per hour. Time to fill = 75/2 = 37.5 hours.

Speed, Distance & Algebra

Speed conversion, relative speed of trains, boats and streams, followed by a linear equation and an algebraic identity.

📋 Quick referenceSpeed & Algebra Quick Reference▶
  • Downstream speed = boat speed + stream speed; upstream speed = boat speed - stream speed.
  • x + 1/x = k gives x^2 + 1/x^2 = k^2 - 2; square the identity instead of solving a quadratic.

Set Up the Rate Before Calculating It

For Aspirants

  • For speed problems, write out exactly what's being compared (relative speed, or boat speed vs. stream speed) before calculating.
  • For algebra, try substitution or factorization before expanding a complicated expression.

  1. 1. Two trains 120 m and 180 m long run on parallel tracks in the same direction at 54 km/h and 36 km/h respectively. Find the time taken by the faster train to completely cross the slower train.

    ▶Reveal answer
    60 seconds

    Relative speed = 54 − 36 = 18 km/h = 18 × (5/18) = 5 m/s. Total length to be crossed = 120 + 180 = 300 m, so time = 300/5 = 60 seconds.

  2. 2. A boat travels 36 km downstream in 3 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water.

    ▶Reveal answer
    10.5 km/h

    Downstream speed = 36/3 = 12 km/h; upstream speed = 36/4 = 9 km/h. Speed in still water = (12 + 9)/2 = 10.5 km/h.

  3. 3. If 3x + 7 = 2x + 15, find the value of x.

    ▶Reveal answer
    x = 8

    Moving terms: 3x − 2x = 15 − 7, which gives x = 8. Substituting back confirms both sides equal 31.

  4. 4. If x + 1/x = 5, find the value of x² + 1/x².

    ▶Reveal answer
    23

    Squaring both sides of x + 1/x = 5 gives x² + 2 + 1/x² = 25. Subtracting 2 gives x² + 1/x² = 23.

Geometry & Mensuration

Triangle area, circle circumference, rhombus perimeter, and area/volume mensuration (cuboids, cylinders, trapeziums).

📋 Quick referenceGeometry & Mensuration Quick Reference▶
  • For a non-right-angled triangle with three known sides, use Heron's formula.
  • Volume of a cuboid = length x breadth x height; curved surface area of a cylinder = 2 x pi x r x h.

Sketch First, Keep a Formula Sheet

For Aspirants

  • Draw a rough sketch first for geometry and mensuration, labeling the given sides or angles.
  • Keep a personal one-page formula reference (area, volume) for quick review before the exam.

  1. 1. The radius of a circle is 21 cm. Find its circumference. (Use π = 22/7)

    ▶Reveal answer
    132 cm

    Circumference = 2πr = 2 × (22/7) × 21. Since 21/7 = 3, this gives 2 × 22 × 3 = 132 cm.

  2. 2. The diagonals of a rhombus measure 24 cm and 10 cm. Find the perimeter of the rhombus.

    ▶Reveal answer
    52 cm

    Half-diagonals are 12 cm and 5 cm, meeting at right angles. Side = √(12² + 5²) = √169 = 13 cm, so perimeter = 4 × 13 = 52 cm.

  3. 3. Find the volume of a cuboid with length 12 cm, breadth 8 cm, and height 6 cm.

    ▶Reveal answer
    576 cm³

    Volume of a cuboid = length × breadth × height = 12 × 8 × 6 = 576 cm³.

  4. 4. Find the curved surface area of a cylinder with radius 7 cm and height 10 cm. (Use π = 22/7)

    ▶Reveal answer
    440 cm²

    Curved surface area = 2πrh = 2 × (22/7) × 7 × 10. Since 7/7 = 1, this simplifies to 2 × 22 × 10 = 440 cm².

  5. 5. Find the area of a trapezium whose parallel sides are 15 cm and 25 cm, and whose height is 8 cm.

    ▶Reveal answer
    160 cm²

    Area = (1/2) × (sum of parallel sides) × height = (1/2) × (15 + 25) × 8 = (1/2) × 40 × 8 = 160 cm².

Trigonometry, Statistics & Data Interpretation

Trigonometric ratios and heights-and-distances, statistical measures like mean, median and range, and a table-based data interpretation question.

📋 Quick referenceTrigonometry, Statistics & DI Quick Reference▶
  • tan(theta) = opposite/adjacent; sin^2(theta) + cos^2(theta) = 1.
  • Mean = sum of values / count; sort the data set first for median and range questions.

Standard Ratios, Sorted Data, One Careful Read

For Aspirants

  • For statistics questions, identify whether the prompt asks for a central value or spread before calculating.
  • For table or graph-based DI, read the whole dataset once before calculating anything.

  1. 1. The angle of elevation of the top of a tower from a point on the ground 60 m away from its base is 30°. Find the height of the tower. (Use √3 = 1.732)

    ▶Reveal answer
    20√3 m ≈ 34.64 m

    Using tan 30° = height/distance, height = 60 × tan 30° = 60 × (1/√3) = 60√3/3 = 20√3. With √3 = 1.732, this is about 34.64 m.

  2. 2. In a right-angled triangle, if cos θ = 3/5, find the value of tan θ.

    ▶Reveal answer
    4/3

    Using a 3-4-5 right triangle, if the adjacent side is 3 and hypotenuse is 5, the opposite side is √(5²−3²) = 4. So tan θ = opposite/adjacent = 4/3.

  3. 3. Find the mean of the first 10 even natural numbers.

    ▶Reveal answer
    11

    The first 10 even numbers are 2, 4, ..., 20, summing to (2+20)×10/2 = 110. Mean = 110/10 = 11.

  4. 4. Find the median of the following data set: 12, 18, 9, 25, 15, 20, 10.

    ▶Reveal answer
    15

    Arranging in order: 9, 10, 12, 15, 18, 20, 25. With 7 values, the median is the 4th term, which is 15.

  5. 5. The marks obtained by 8 students in a test are: 45, 62, 38, 55, 70, 41, 58, 49. Find the range of the data.

    ▶Reveal answer
    32

    Range = highest value − lowest value. The highest mark is 70 and the lowest is 38, so the range = 70 − 38 = 32.

  6. 6. The following table shows the number of tickets sold by a railway counter over four days: Monday - 320, Tuesday - 275, Wednesday - 410, Thursday - 350. What is the average number of tickets sold per day over these four days?

    ▶Reveal answer
    338.75

    Total tickets sold = 320 + 275 + 410 + 350 = 1,355. Average per day = 1,355 / 4 = 338.75.

Time-traps & syllabus quirks

  • With a -1/3 mark penalty, guessing blindly on a question you never attempted costs more than skipping it. The better habit is to solve every question you're confident about first, then return to the harder ones only if time remains.
  • In compound interest problems, a common silent error is mismatching the rate and time period, for example using an annual rate directly when interest is actually compounded half-yearly. The formula can be applied correctly and still give a wrong answer if this mismatch is missed.

Frequently asked questions

How many questions does RRB NTPC Mathematics have?

30 questions in CBT 1 (35 in CBT 2), each worth 1 mark, with 1/3 mark deducted for every wrong answer.

What's a realistic target score for RRB NTPC Maths?

24-27 out of 30 is a strong target, since the questions themselves are rarely difficult; the section rewards speed and accuracy over advanced knowledge.

Score well here, and a Railway or SSC MTS government role moves within real reach. Keep drilling.

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