The role of Mathematics in railway CBTs
Mathematics has 30 questions in the NTPC CBT-1 and, as reported, 25 in the Group D CBT, each carrying one mark with a one-third deduction for a wrong answer, inside a single 90-minute test. At about 54 seconds a question for the whole paper, Mathematics questions need to be answered in 45 to 70 seconds so that other sections get their share. The questions are direct: they rarely need a deep idea, but they reward speed and cleanly remembered methods. Because competition is intense, a few extra correct answers in Mathematics can move you across a cut-off.
Topic map
| Area | Topics | Nature of questions |
|---|---|---|
| Number system and simplification | HCF and LCM, divisibility, BODMAS, fractions, decimals, squares and roots | Quick; memory-based |
| Arithmetic | Percentage, ratio and proportion, averages, profit and loss, discount, simple and compound interest, ages, partnership, mixtures | Largest share; formula and shortcut questions |
| Time-based problems | Time and work, pipes and cisterns, time, speed and distance, trains, boats and streams | Rate thinking |
| Algebra | Linear equations, basic identities, simple quadratics | Short |
| Geometry and mensuration | Triangles, circles, quadrilaterals, areas, perimeters, volumes | Formula-based |
| Trigonometry and data | Basic ratios and identities; tables and charts; statistics basics | Short |
Check the syllabus in the CEN of your recruitment; the mix varies.
What the questions look like
Percentage. A price rises from 80 to 92. What is the percentage increase? 12 ÷ 80 = 15%.
HCF and LCM. Find the HCF and LCM of 36 and 48. HCF = 12 and LCM = 144 (check: 12 × 144 = 1,728 = 36 × 48).
Time and work. A can do a job in 12 days and B in 24 days. Together? The rates are 1/12 + 1/24 = 3/24 = 1/8, so 8 days.
Time, speed and distance. A train 120 m long passes a pole in 6 seconds. What is its speed in km/h? 120 ÷ 6 = 20 m/s, and 20 × 18 ÷ 5 = 72 km/h.
Simple interest. What is the simple interest on 5,000 at 8% for 3 years? 5,000 × 8 × 3 ÷ 100 = 1,200.
Mensuration. The sides of a rectangle are 24 m and 15 m. What are the area and perimeter? 360 sq m and 78 m.
Average. The average of five numbers is 24; a sixth number raises the average to 26. What is the sixth number? The new total is 156 and the old total is 120, so the sixth number is 36.
Each takes 30 to 60 seconds with the right method. The railway-specific twist appears in the context, such as trains and platforms, so practise time, speed and distance thoroughly.
Speed methods worth learning
- Fractions for percentages (12.5% = 1/8, 16.67% = 1/6, 33.33% = 1/3).
- Multiplying factors for successive changes.
- Work as units: take the LCM of days as the total work.
- km/h to m/s: multiply by 5/18; reverse by 18/5.
- Squares to 30 and cubes to 15, and tables to 20. See squares, cubes and roots practice.
- Elimination by units and range when options are far apart.
More are in mental maths techniques.
Time management
| Stage | Time (30-question section) | What to do |
|---|---|---|
| First pass | About 24 minutes | Solve questions where the method is clear in 5 seconds; mark others |
| Second pass | About 6 minutes | Return to marked questions in order of ease |
| Check | Within the overall review | Verify arithmetic on doubtful answers |
In a 90-minute CBT you have one clock, so time saved in Mathematics can be used for review at the end. Set a cap of about 70 seconds per question on the first pass. See how to pick which questions to skip.
Negative marking in Mathematics
With a one-third penalty, the break-even accuracy is 25%. For a question where you have narrowed the options to two, an attempt has an expected gain of (½ × 1) − (½ × ⅓) = +0.33. For a question with no elimination, the expected gain is zero. Because Mathematics questions are computational, a computed answer that matches no option usually means a slip, not a guess to be made. Track net marks from guessed Mathematics answers separately. See our negative marking guide.
How to practise
- Topic sets (10 to 15 questions): daily in the early phase, at 45 seconds each.
- Calculation drills: ten minutes a day on tables, squares and fractions.
- Sectionals (30 questions in 32 minutes): two a week in the middle phase.
- Full CBTs: weekly in the last two months.
Our topic pages include percentage, profit and loss, averages, ratio and proportion, HCF and LCM, time and work and mensuration.
Analysing your Mathematics result
| Pattern | Probable cause | Action |
|---|---|---|
| Errors concentrated in one topic | Concept gap | Topic repair: 15 questions within a week |
| Right method, wrong number | Arithmetic slips | Tables and squares; check the last step |
| Cannot finish the section | Slow methods | Learn shortcuts; cap at 70 seconds |
| Wrong answers on word problems | Misreading | Underline the ask and the units |
| Guessed answers losing marks | Guessing without elimination | Compute net marks by topic |
Common mistakes in railway Mathematics preparation
- Spending time on advanced problems that do not appear.
- Learning shortcuts without understanding them.
- Not memorising tables, squares and fractions.
- Practising untimed.
- Skipping geometry and mensuration formulas.
Related pages
See the railway hub, the exam pattern and the mock test strategy. Other sections: Reasoning and General Awareness. For a worked review read how to use mock tests for railway exams. Mathematics tests published by institutes appear below.
Note: the section sizes above reflect the NTPC CBT-1 and reported Group D patterns; confirm them in the CEN of your recruitment.