About this RRB NTPC Math practice test

RRB NTPC Mathematics is a 30-mark section in CBT 1 (35 in CBT 2) that covers Number System, Arithmetic, Simple and Compound Interest, Time-Work-Pipes, Time-Speed-Distance, Algebra, Geometry, Mensuration, Trigonometry, and elementary Statistics. With negative marking in effect, accuracy matters as much as speed — a prepared candidate who avoids silly errors across 25 questions gains more than one who rushes all 30 under the clock. This practice test is useful for RRB NTPC, RRB Group D, RRB ALP, SSC MTS and all other Railway and competitive exams with a Mathematics section.

RRB NTPC Mathematics Practice Test sample questions

These starter questions help you launch a math mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

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

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

3. 3. Simplify: √50 + √18 − √8.

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

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

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

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

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

9. 9. At what rate of simple interest per annum will a sum of Rs. 4200 amount to Rs. 5040 in 4 years?

10. 10. 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?

11. 11. A is twice as efficient as B. Working together, they complete a work in 10 days. In how many days can A alone complete the work?

12. 12. 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?

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

14. 14. 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.

15. 15. 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.

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

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

18. 18. The sum of two numbers is 45 and their difference is 9. Find the larger number.

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

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

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

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

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

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

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

26. 26. 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)

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

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

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

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

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

1. 1. LCM of 36 and 84

   252

   Prime factorize: 36 = 2² × 3² and 84 = 2² × 3 × 7. The LCM takes the highest power of each prime, giving 2² × 3² × 7 = 252. Check: HCF = 2² × 3 = 12, and 12 × 252 = 3024 = 36 × 84, confirming the answer.

2. 2. Fraction expression with LCM 12

   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.

3. 3. Simplifying surds √50+√18−√8

   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.

4. 4. Percentage scored (432/600)

   72%

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

5. 5. Profit percent (CP 750, SP 900)

   20%

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

6. 6. Ratio of ages 4:5, sum 54

   30 years

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

7. 7. Simple interest, Rs.8000, 9%, 3 yrs

   Rs. 2160

   SI = (P × R × T)/100 = (8000 × 9 × 3)/100 = 216000/100 = Rs. 2160.

8. 8. Compound interest, Rs.5000, 10%, 2 yrs

   Rs. 1050

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

9. 9. Rate of SI, 4200 to 5040 in 4 yrs

   5% per annum

   SI earned = 5040 − 4200 = Rs. 840. Rate = (SI × 100)/(P × T) = (840 × 100)/(4200 × 4) = 84000/16800 = 5%.

10. 10. A(12 days) and B(18 days) together

    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.

11. 11. A twice as efficient as B, together 10 days

    15 days

    Let B's one-day work be x, so A's is 2x; together 3x = 1/10, giving x = 1/30. A's one-day work = 2/30 = 1/15, so A alone takes 15 days.

12. 12. Pipe fills 15 hrs, pipe empties 25 hrs

    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.

13. 13. Speed of car in m/s (250 km in 5 hr)

    ≈13.89 m/s (125/9 m/s)

    Speed = 250 km/5 h = 50 km/h. Converting to m/s: 50 × (5/18) = 250/18 = 125/9 ≈ 13.89 m/s.

14. 14. Two trains, same direction crossing time

    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.

15. 15. Boat speed in still water

    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.

16. 16. Solve 3x+7 = 2x+15

    x = 8

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

17. 17. x+1/x=5, find x²+1/x²

    23

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

18. 18. Sum 45, difference 9, larger number

    27

    Larger number = (sum + difference)/2 = (45 + 9)/2 = 27. The smaller number is (45 − 9)/2 = 18, and 27 + 18 = 45 checks out.

19. 19. Area of triangle with sides 7,24,25

    84 cm²

    Check for a right triangle: 7² + 24² = 49 + 576 = 625 = 25², so it is right-angled with legs 7 and 24. Area = (1/2) × 7 × 24 = 84 cm².

20. 20. Circumference of circle, radius 21 cm

    132 cm

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

21. 21. Perimeter of rhombus, diagonals 24 & 10

    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.

22. 22. Volume of cuboid 12×8×6

    576 cm³

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

23. 23. CSA of cylinder, r=7, h=10

    440 cm²

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

24. 24. Area of trapezium, parallel sides 15 & 25, height 8

    160 cm²

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

25. 25. sin60·cos30 + sin30·cos60

    1

    sin 60° × cos 30° = (√3/2)(√3/2) = 3/4, and sin 30° × cos 60° = (1/2)(1/2) = 1/4. Adding gives 3/4 + 1/4 = 1, consistent with sin(60°+30°) = sin 90° = 1.

26. 26. Height of tower, angle of elevation 30°, distance 60 m

    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.

27. 27. cos θ = 3/5, find tan θ

    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.

28. 28. Mean of first 10 even natural numbers

    11

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

29. 29. Median of 12,18,9,25,15,20,10

    15

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

30. 30. Range of marks data set

    32

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

Curriculum Mapping & Learning Guide

Use this breakdown to identify which skills each question tests and guide post-test review.

RRB NTPC Math units covered

1. Chapter 1: Number System (LCM, HCF, Fractions, Surds)
2. Chapter 2: Arithmetic (Percentage, Profit/Loss, Ratio)
3. Chapter 3: Simple and Compound Interest
4. Chapter 4: Time, Work and Pipes
5. Chapter 5: Time, Speed and Distance
6. Chapter 6: Algebra (Equations and Identities)
7. Chapter 7: Geometry (Triangles, Circles, Quadrilaterals)
8. Chapter 8: Mensuration (Area and Volume)
9. Chapter 9: Trigonometry (Ratios and Heights & Distances)
10. Chapter 10: Statistics (Mean, Median, Mode, Range)

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