RRB NTPC Maths Formulas: What You Need
RRB NTPC CBT 1 has 30 Mathematics questions out of 100 (with 30 General Intelligence and 40 General Awareness) in 90 minutes, and every wrong answer costs 1/3 mark. The maths is Class 10 level and mostly arithmetic: percentage, profit and loss, simple and compound interest, ratio, time and work, speed and trains, averages, mensuration and number system. If you know the formulas below and can apply them in under a minute, you can attempt almost the whole section.
Key takeaway: About two-thirds of RRB NTPC maths questions are direct formula applications. Learn this sheet, practise 10 questions a day on each chapter, and attempt only those you can finish; skipping costs nothing, a wrong guess costs 1/3 mark.
Every worked answer on this page was computed in Python before publishing.
RRB NTPC Maths Syllabus and Chapter-Wise Weightage
| Chapter | Typical questions (CBT 1) | Formula load |
|---|---|---|
| Number system, LCM and HCF, divisibility | 3–4 | Medium |
| Simplification, BODMAS, surds and indices | 2–3 | Low |
| Percentage, profit and loss, discount | 4–5 | High |
| Simple and compound interest | 2–3 | High |
| Ratio, proportion, ages, mixtures | 3–4 | Medium |
| Time and work, pipes and cisterns | 2–3 | Medium |
| Time, speed and distance, trains, boats | 3–4 | High |
| Averages | 1–2 | Low |
| Mensuration (2D and 3D) | 2–3 | High |
| Algebra, geometry, trigonometry, statistics | 3–4 | Medium |
The counts are a typical spread seen across recent shifts, not an official split; RRB publishes only the section total (30).
Percentage, Profit and Loss Formulas for RRB NTPC
| Formula | Use |
|---|---|
| x% of y = (x × y) ÷ 100 | Basic percentage |
| % change = (change ÷ original) × 100 | Increase or decrease |
| If price rises by r%, cut consumption by r ÷ (100 + r) × 100% to keep spend same | Price–consumption |
| Successive change a% and b% = a + b + (a × b) ÷ 100 | Use minus sign for a fall |
| Profit % = (SP − CP) ÷ CP × 100 | Profit always on CP |
| SP = CP × (100 + P%) ÷ 100 | Selling price from profit |
| Discount % = (MP − SP) ÷ MP × 100 | Discount always on MP |
| Two discounts d₁, d₂ → single = d₁ + d₂ − (d₁ × d₂) ÷ 100 | Successive discounts |
Example: Price of sugar rises by 25%. By how much should a family cut consumption to keep expense the same? 25 ÷ 125 × 100 = 20%.
Example: Successive discounts of 20% and 10% equal 20 + 10 − 2 = 28%.
Simple Interest and Compound Interest Formulas
| Formula | Note |
|---|---|
| SI = (P × R × T) ÷ 100 | Interest grows by the same amount every year |
| Amount (CI) = P × (1 + R/100)ᵀ | Compounded yearly |
| Half-yearly: rate R/2, time 2T | Quarterly: R/4, 4T |
| CI − SI for 2 years = P × (R/100)² | Most asked shortcut |
| CI − SI for 3 years = P × (R/100)² × (3 + R/100) | |
| Sum doubles in T years at SI → R = 100 ÷ T |
Example: ₹12,000 at 8% SI for 3 years gives 12000 × 8 × 3 ÷ 100 = ₹2,880.
Example: CI on ₹10,000 at 10% for 2 years = 10000 × 1.21 − 10000 = ₹2,100. CI − SI = 10000 × 0.01 = ₹100.
Time and Work and Pipes Formulas for RRB NTPC
- If A finishes a job in a days, A's one-day work = 1/a.
- A and B together: time = (a × b) ÷ (a + b).
- Work = efficiency × time; when efficiency ratio is m : n, time ratio is n : m.
- Pipes: filling pipe is +, emptying pipe (leak) is −. A fills in a hours, B empties in b hours → net time = (a × b) ÷ (b − a).
- Men–days rule: M₁ × D₁ × H₁ ÷ W₁ = M₂ × D₂ × H₂ ÷ W₂.
Example: A does a job in 12 days, B in 18 days. Together: (12 × 18) ÷ 30 = 216 ÷ 30 = 7.2 days (7 1/5 days).
Time, Speed, Distance and Train Formulas
| Formula | Use |
|---|---|
| Speed = Distance ÷ Time | Basic |
| km/h → m/s: × 5/18; m/s → km/h: × 18/5 | Always convert first |
| Average speed (equal distances) = 2xy ÷ (x + y) | Not (x + y) ÷ 2 |
| Train crosses a pole or man: time = train length ÷ speed | |
| Train crosses platform or bridge: time = (train + platform) ÷ speed | |
| Two trains opposite directions: relative speed = sum; same direction = difference | |
| Boat: downstream = u + v, upstream = u − v; u = (D + U) ÷ 2, v = (D − U) ÷ 2 |
Example: A 240 m train at 72 km/h (= 20 m/s) passes a pole in 240 ÷ 20 = 12 seconds.
Example: A 300 m train at 54 km/h (= 15 m/s) crosses a 450 m platform in 750 ÷ 15 = 50 seconds.
Mensuration Formulas for RRB NTPC (2D and 3D)
| Shape | Area / Volume | Perimeter / Surface area |
|---|---|---|
| Rectangle | l × b | 2(l + b) |
| Square | a² | 4a; diagonal a√2 |
| Triangle | ½ × base × height; Heron: √[s(s−a)(s−b)(s−c)] | a + b + c |
| Equilateral triangle | (√3/4)a² | 3a |
| Circle | πr² | 2πr |
| Cube | a³ | TSA 6a² |
| Cuboid | l × b × h | TSA 2(lb + bh + hl) |
| Cylinder | πr²h | CSA 2πrh; TSA 2πr(r + h) |
| Cone | ⅓πr²h | CSA πrl, l = √(r² + h²) |
| Sphere | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | CSA 2πr², TSA 3πr² |
Example: Cylinder with r = 7 cm, h = 10 cm: 22/7 × 49 × 10 = 1,540 cm³.
Number System, Average and Ratio Formulas
- Sum of first n natural numbers = n(n + 1) ÷ 2; squares = n(n + 1)(2n + 1) ÷ 6; cubes = [n(n + 1) ÷ 2]².
- Product of two numbers = HCF × LCM.
- Divisibility by 11: (sum of odd-place digits) − (sum of even-place digits) is 0 or a multiple of 11.
- Average = sum ÷ count; average of first n natural numbers = (n + 1) ÷ 2.
- Dividing an amount in ratio a : b → shares = a ÷ (a + b) and b ÷ (a + b) of the total.
Example: HCF 12, LCM 180, one number 36 → other = 12 × 180 ÷ 36 = 60.
RRB NTPC Maths Questions with Answers (Practice Set)
- A sum of ₹640 is divided in the ratio 3 : 5. Find the larger share. Answer: ₹400. 640 × 5/8.
- An article bought for ₹640 is sold for ₹800. Profit %? Answer: 25%. 160 ÷ 640 × 100.
- Average of the first 25 natural numbers? Answer: 13. (25 + 1) ÷ 2.
- A man goes at 60 km/h and returns at 40 km/h. Average speed? Answer: 48 km/h. 2 × 60 × 40 ÷ 100.
- Difference between CI and SI on ₹5,000 at 10% for 2 years? Answer: ₹50. 5000 × (1/10)².
- Pipe A fills a tank in 20 min; pipe B empties it in 30 min. Both open: time to fill? Answer: 60 min. 20 × 30 ÷ 10.
- A boat goes 18 km/h downstream and 12 km/h upstream. Speed of stream? Answer: 3 km/h. (18 − 12) ÷ 2.
- Is 918082 divisible by 11? Answer: Yes. Digits in places 1, 3, 5 from the left: 9 + 8 + 8 = 25; places 2, 4, 6: 1 + 0 + 2 = 3; difference 22 is a multiple of 11.
- 50 L of milk–water mixture is 7 : 3. How much water to add to make it 7 : 5? Answer: 10 L. Milk 35 L; water needed 35 × 5/7 = 25 L; already 15 L.
- Ages of A and B are 4 : 5. After 6 years they will be 5 : 6. Present age of B? Answer: 30 years. 4x + 6 : 5x + 6 = 5 : 6 → x = 6.
Common Mistakes in RRB NTPC Maths
- Forgetting to convert km/h to m/s in train questions.
- Taking profit % on SP or discount % on CP.
- Using (x + y) ÷ 2 for average speed over equal distances.
- Adding successive percentages directly (20% + 10% is not 30%).
- Using π = 3.14 when options are built on 22/7 (check the options first).
RRB NTPC Maths Formulas FAQs
How many maths questions come in RRB NTPC CBT 1?
30 out of 100 questions, in 90 minutes, shared with 30 General Intelligence and Reasoning and 40 General Awareness questions.
Is there negative marking in RRB NTPC?
Yes. One-third of the marks for a question are deducted for each wrong answer.
Which maths topics are most important for RRB NTPC 2026?
Percentage, profit and loss, SI and CI, time and work, speed and trains, ratio, averages and mensuration. These arithmetic chapters make up most of the section.
Is the RRB NTPC maths level hard?
No. It is around Class 10 level. Speed and accuracy matter more than advanced concepts.
Is RRB NTPC maths the same as RRB Group D maths?
The chapters are almost the same; NTPC Graduate level has slightly more data interpretation and algebra. Group D has 25 maths questions out of 100.
Practice Next
- Railway maths practice (RRB JE and ALP CBT-1 use the same arithmetic): RRB JE Maths Mock Test 01, RRB JE Maths Mock Test 02, RRB ALP Maths Mock Test 01 and RRB ALP Maths Mock Test 02.
- Mock tests: RRB NTPC Mathematics Sectional Mock Test 01, RRB NTPC Maths Mini Quiz 01, RRB NTPC Maths Mini Quiz 02 and RRB NTPC CBT 1 Full Mock Test 01.
- Job update: RRB NTPC 2026 notification.
- Related notes: percentage tricks, time and work tricks, mensuration formulas, SI and CI difference formula, biology for RRB Group D and Indian railway zones and headquarters.
- Browse all study notes.