In this guide
Mathematics in RRB NTPC is not about hard proofs. It is about solving school-level problems quickly and accurately. There are 30 questions in CBT 1 and 35 in CBT 2, and this is the section where most candidates run out of time.
The good news: the same handful of arithmetic ideas returns again and again. A candidate who knows six or seven methods deeply, and has practised them under a timer, can answer most questions in under a minute.
What the syllabus covers
Recent notices have listed: number system, decimals, fractions, LCM and HCF, ratio and proportion, percentage, mensuration, time and work, time and distance, simple and compound interest, profit and loss, elementary algebra, geometry and trigonometry, and elementary statistics.
Topic priority
| Priority | Topics |
|---|---|
| High | Number system, simplification, percentage, ratio and proportion, averages, profit and loss, simple and compound interest, time and work, time and distance, trains |
| Medium | Mensuration, algebra, ages, mixtures, pipes and cisterns, boats and streams |
| Lower | Geometry, trigonometry, statistics and data interpretation |
"Lower" does not mean "skip". It means "study after the high-priority topics are strong". Arithmetic comes first because it is the base for everything else: a mensuration question is often a percentage question in disguise.
A six-week order
| Week | Topics |
|---|---|
| 1 | Number system, LCM–HCF, simplification, squares and tables |
| 2 | Percentage, ratio and proportion, averages |
| 3 | Profit, loss and discount; simple and compound interest |
| 4 | Time and work, pipes and cisterns, time and distance, trains, boats |
| 5 | Ages, mixtures, algebra, mensuration |
| 6 | Geometry, trigonometry, statistics; mixed practice |
After six weeks, keep one mixed practice session every day until the exam. Start with the number system guide and percentage.
A daily routine (60 to 90 minutes)
- 10 minutes: mental calculation: tables, squares, fraction-percentage pairs.
- 30 minutes: learn or revise one topic; solve 15 to 20 questions.
- 20 minutes: 10 to 15 mixed questions from earlier topics, with a timer.
- 10 minutes: check answers; write every mistake in an error notebook.
Build calculation speed
Learn by heart: tables up to 20, squares up to 30, cubes up to 15, and these fraction-percentage pairs.
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/7 | 14 2/7% |
| 1/3 | 33 1/3% | 1/8 | 12.5% |
| 1/4 | 25% | 1/9 | 11 1/9% |
| 1/5 | 20% | 1/10 | 10% |
| 1/6 | 16 2/3% | 1/12 | 8 1/3% |
Six methods that save time, and why they work
A shortcut used without understanding fails the moment a question is phrased differently. For each method below, know the reason.
1. Switch percentages to fractions. 12.5% of 480 is 480 ÷ 8 = 60. Why it works: a percentage is a fraction of 100, and 12.5/100 = 1/8. Dividing by 8 is faster than multiplying by 0.125.
2. Successive percentage change: a + b + ab/100. For changes of a% and then b% (use a minus sign for a fall), the net change is a + b + ab/100. Why it works: the multiplier is (1 + a/100)(1 + b/100) = 1 + a/100 + b/100 + ab/10,000. Subtract 1 and multiply by 100.
3. Unit method for ratios. If money is shared 2 : 3 : 4, there are 9 equal parts. Find one part, then multiply. Why it works: a ratio only tells you how many equal parts each person gets.
4. LCM method for time and work. Take the total work as the LCM of the days. Why it works: you can call the work any amount, and choosing one that every time divides evenly gives whole-number daily rates. See time and work.
5. km/h to m/s: multiply by 5/18. Why it works: 1 km/h = 1,000 m ÷ 3,600 s = 5/18 m/s. Going back, multiply by 18/5.
6. Check with digit sums. To check 47 × 23 = 1,081: 4 + 7 = 11, then 1 + 1 = 2; 2 + 3 = 5; 2 × 5 = 10, then 1 + 0 = 1. And 1 + 0 + 8 + 1 = 10, then 1. They match. Why it works: every power of 10 leaves remainder 1 when divided by 9, so a number and its digit sum leave the same remainder. It will not catch two digits swapped, so treat it as a quick check, not proof.
Two more calculation tricks that are worth ten seconds each:
- Near 100: 97 × 96. Take 100 − 3 − 4 = 93 and 3 × 4 = 12, giving 9,312. Why: (100 − a)(100 − b) = 100(100 − a − b) + ab.
- Near 50: 48² = (50 − 2)² = 2,500 − 200 + 4 = 2,304.
Worked questions at NTPC level
Q1. The price of an item rises by 25% and then falls by 20%. What is the net change?
Using a + b + ab/100: 25 − 20 + (25 × −20)/100 = 5 − 5 = 0, no change.
Check: 100 → 125 → 125 − 25 = 100.
Q2. ₹5,400 is divided among A, B and C in the ratio 2 : 3 : 4. How much does C get?
Parts: 2 + 3 + 4 = 9. One part: 5,400 ÷ 9 = 600. C gets 4 × 600 = ₹2,400.
Q3. A can finish a job in 12 days and B in 18 days. In how many days can they finish it together?
LCM of 12 and 18 = 36 units of work. A does 36 ÷ 12 = 3 units a day, B does 36 ÷ 18 = 2.
Together: 5 units a day, so 36 ÷ 5 = 7 1/5 days.
Q4. A train 240 m long runs at 54 km/h. How long does it take to cross a platform 210 m long?
Distance to cover: 240 + 210 = 450 m (the whole train must clear the platform).
Speed: 54 × 5/18 = 15 m/s. Time: 450 ÷ 15 = 30 seconds.
Q5. A shopkeeper marks an article at ₹960, gives a 25% discount and still makes a 20% profit. Find the cost price.
Selling price: 960 × 75/100 = ₹720. Profit 20% means SP = 1.2 × CP.
CP = 720 ÷ 1.2 = ₹600.
Q6. The average of five numbers is 24. When one number is removed, the average of the rest is 22. Which number was removed?
Total of five: 5 × 24 = 120. Total of four: 4 × 22 = 88.
Removed number: 120 − 88 = 32.
Common errors
- Mixed units: km/h with metres, or hours with minutes.
- Wrong base for a percentage: profit is on cost price; discount is on marked price.
- Adding successive percentages: a 20% rise then a 20% fall is a 4% loss, not zero.
- Copying a number wrongly from the screen to the rough sheet.
- Answering the wrong thing: finding the cost price when the question asked for profit.
Practice set
- A number is increased by 30% and then decreased by 30%. Find the net change.
- A can do a job in 10 days and B in 15 days. How long will they take together?
- Convert 72 km/h into m/s.
- A train 150 m long passes a pole in 9 seconds. Find its speed in km/h.
- Find the simple interest on ₹4,000 at 8% a year for 3 years.
- An article bought for ₹450 is sold for ₹540. Find the profit percentage.
- Two numbers are in the ratio 3 : 5 and their sum is 96. Find their difference.
- Find 12.5% of 480.
Answers:
- 9% decrease. 30 − 30 + (30 × −30)/100 = −9. Check: 100 → 130 → 91.
- 6 days. LCM 30; A does 3 units a day, B does 2; 30 ÷ 5 = 6.
- 20 m/s. 72 × 5/18 = 20.
- 60 km/h. 150 ÷ 9 = 50/3 m/s; 50/3 × 18/5 = 60.
- ₹960. 4,000 × 8 × 3 ÷ 100 = 960.
- 20%. Profit 90; 90 ÷ 450 × 100 = 20.
- 24. One part = 96 ÷ 8 = 12; numbers 36 and 60; difference 2 parts = 24.
- 60. 12.5% = 1/8, and 480 ÷ 8 = 60.
Self-check after six weeks
- I know tables to 20, squares to 30 and cubes to 15.
- I can solve a percentage or ratio question in under 45 seconds.
- I have solved past RRB NTPC questions for every topic.
- My accuracy in mixed timed practice is above 85%.
- My error notebook has a fix written next to every mistake.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
Get the next RRB NTPC guide by email
New guides every week. No spam, unsubscribe any time.