Maths Formulas for Competitive Exams: Tricks & Examples
PratapSolution • Exam Prep 2026
Maths Formula Sheet 2026: 25 Topics for SSC, RRB & Banking
Formula → solved example → memory trick. A bright, simple revision guide to refresh competitive-exam Maths without wading through lengthy theory.
Preparing for SSC, RRB NTPC, CONCOR, Banking or another competitive exam? Use this last-minute Maths formula capsule to revise percentages, ratio, profit and loss, interest, algebra, trains, geometry and more. Each topic includes a quick formula, a worked exam-style example and a common mistake to avoid.
Important: This guide includes original exam-style examples, not verbatim previous-year questions or a verified ranking of the “most repeated” questions. Different exams have different syllabi. Prioritize the topics that appear in your own exam notice.
Before You Start: The 5-Minute Calculation Toolkit
These values help reduce calculation time in many aptitude questions. Revise them before opening the 25 topic cards.
Fraction → Percentage
| Fraction | Percent |
|---|---|
| 1/2 | 50% |
| 1/3 | 33⅓% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16⅔% |
| 1/8 | 12.5% |
| 3/4 | 75% |
Shortcut: 12.5% of 640 = 640 ÷ 8 = 80.
Squares, Cubes & Roots
| Number | Square | Cube |
|---|---|---|
| 5 | 25 | 125 |
| 8 | 64 | 512 |
| 10 | 100 | 1,000 |
| 12 | 144 | 1,728 |
| 15 | 225 | 3,375 |
| 20 | 400 | 8,000 |
| 25 | 625 | 15,625 |
Shortcut: 35² → 3×4 = 12, append 25 → 1225. Remember √2025 = 45.
Start here: these formulas combine well with most railway, SSC and banking quantitative aptitude questions.Part 1: High-Scoring Arithmetic
01
Percentage
Must-remember formula
Percentage = (Part ÷ Total) × 100
Change % = (Change ÷ Original value) × 100
Successive change % = a + b + ab/100 (decrease = negative)
Exam-style example
A price rises by 20% and then falls by 10%. Net change?
20 − 10 − (20 × 10)/100 = 8% increase.
Remember: Start from 100 when changes happen one after another.
Avoid this mistake: An increase of x% followed by a decrease of x% gives a loss of x²/100%, not zero.
02
Ratio & Proportion
Must-remember formula
a:b = a/b
If a:b = c:d, then ad = bc
Share = Total × Required parts ÷ Sum of parts
Exam-style example
Divide ₹840 in the ratio 3:4. Find the smaller share.
Total parts = 7; smaller share = 840 × 3/7 = ₹360.
Remember: Add parts → calculate one part → distribute.
Avoid this mistake: Make the shared term equal before combining A:B and B:C.
03
Average
Must-remember formula
Average = Sum of values ÷ Number of values
New average after replacing one value = Old average + (New − Old)/n
Combined average = (n₁A₁ + n₂A₂)/(n₁+n₂)
Exam-style example
12 students average 24 marks; 3 more students average 36. New average?
24 + [(36 − 24) × 3/15] = 26.4.
Remember: For changes, adjust the average; do not recalculate every total.
Avoid this mistake: Do not take the simple mean of two group averages unless group sizes match.
04
Profit, Loss & Discount
Must-remember formula
Profit = SP − CP; Loss = CP − SP
Profit % = Profit/CP × 100; Loss % = Loss/CP × 100
Discount % = (MP − SP)/MP × 100
SP at x% profit = CP × (100+x)/100
Exam-style example
An item is marked 40% above cost, then discounted by 20%. Profit %?
Assume CP = ₹100 → MP = ₹140 → SP = ₹112 → 12% profit.
Remember: Profit/loss uses CP; discount uses marked price (MP).
Avoid this mistake: Two percentage changes act on different bases; never simply subtract 40 − 20.
05
Simple Interest
Must-remember formula
SI = P × R × T / 100
Amount = Principal + SI
Rate = 100 × SI / (P × T)
Exam-style example
Calculate SI on ₹5,000 at 8% annually for 3 years.
5,000 × 8 × 3 / 100 = ₹1,200.
Remember: If a sum doubles in 8 years at SI, R = 100/8 = 12.5%.
Avoid this mistake: Keep time in years when the rate is per year.
06
Compound Interest
Must-remember formula
Amount = P(1 + R/100)ⁿ (annual compounding)
CI = Amount − P
For 2 years: CI − SI = P(R/100)²
Exam-style example
Find CI on ₹8,000 at 5% for 2 years, compounded annually.
Year 1 = ₹400; year 2 = 5% of ₹8,400 = ₹420; CI = ₹820.
Remember: CI means interest earns more interest.
Avoid this mistake: The two-year CI−SI shortcut assumes annual compounding at a constant rate.
07
Time & Work
Must-remember formula
One-day work by A = 1/a (if A takes a days)
Combined rate = 1/a + 1/b
Together time = ab/(a+b) for two workers working at constant rates
Exam-style example
A finishes in 12 days; B in 18 days. Together?
(12 × 18)/(12 + 18) = 216/30 = 7.2 days.
Remember: Work rate and time are inversely proportional.
Avoid this mistake: If efficiency increases by 20%, completion time does not simply fall by 20%.
08
Pipes & Cisterns
Must-remember formula
Filling rate = +1/a tank/hour
Emptying rate = −1/b tank/hour
Net fill time = 1 ÷ (1/a − 1/b)
Exam-style example
A tap fills a tank in 6 hours and a leak empties it in 9. Both open?
Net rate = 1/6 − 1/9 = 1/18 → 18 hours.
Remember: Fill = plus; leak = minus.
Avoid this mistake: Make sure the net rate is positive if the question asks for the time to fill.
Pick the right distance and units before doing the calculation.Part 2: Speed, Trains & Boats
09
Speed, Distance & Time
Must-remember formula
Speed = Distance/Time
km/h → m/s: ×5/18; m/s → km/h: ×18/5
For equal distances at a and b: average speed = 2ab/(a+b)
Exam-style example
A car goes 120 km at 40 km/h and another 120 km at 60 km/h. Average speed?
Total distance = 240 km; total time = 3 + 2 = 5 h → 48 km/h.
Remember: Average speed always means total distance ÷ total time.
Avoid this mistake: Simple (40+60)/2 = 50 is wrong for equal-distance trips.
10
Trains
Must-remember formula
Crossing a pole: time = Train length/Speed
Crossing a platform: time = (Train + Platform length)/Speed
Opposite direction relative speed = sum; same direction = difference
Exam-style example
A 180 m train crosses a 220 m platform in 20 s. Speed?
(180 + 220)/20 = 20 m/s = 72 km/h.
Remember: Pole = one length; platform = both lengths.
Avoid this mistake: Use metres and seconds together; convert km/h to m/s first.
11
Boats & Streams
Must-remember formula
Downstream = Boat speed + Stream speed
Upstream = Boat speed − Stream speed
Still-water boat speed = (D+U)/2; Stream speed = (D−U)/2
Exam-style example
Downstream speed is 18 km/h and upstream is 12 km/h. Stream speed?
(18 − 12)/2 = 3 km/h.
Remember: With the flow, add; against the flow, subtract.
Avoid this mistake: Do not confuse stream speed with the boat’s speed in still water.
These short rules are useful whenever the paper rewards fast, accurate arithmetic.Part 3: Number System, Algebra & Mental Maths
12
Number System
Must-remember formula
Divisible by 3 or 9: check the sum of digits
Divisible by 4: last 2 digits; by 8: last 3 digits
Divisible by 11: difference of alternating digit sums is a multiple of 11
Exam-style example
Is 4,752 divisible by 8?
Last three digits are 752; 752 ÷ 8 = 94 → Yes.
Remember: Check the smallest relevant digit block before long division.
Avoid this mistake: 1 is neither prime nor composite.
13
HCF & LCM
Must-remember formula
For two positive integers: Product = HCF × LCM
HCF = Greatest common factor
LCM = Smallest common multiple
Exam-style example
HCF = 12, LCM = 360, one integer = 60. Find the other.
(12 × 360)/60 = 72.
Remember: Largest equal group → HCF. Events repeating together → LCM.
Avoid this mistake: The product identity stated here is for two integers.
14
Simplification & BODMAS
Must-remember formula
Brackets and powers first
Multiplication & division: equal priority, left to right
Addition & subtraction: equal priority, left to right
Exam-style example
Simplify 18 + 24 ÷ 6 × 3 − 5.
18 + 4 × 3 − 5 = 18 + 12 − 5 = 25.
Remember: Equal-priority operations are solved from left to right.
Avoid this mistake: BODMAS does not mean all multiplication must happen before division.
15
Algebraic Identities
Must-remember formula
(a+b)² = a² + 2ab + b²
(a−b)² = a² − 2ab + b²
a² − b² = (a−b)(a+b)
a³ + b³ = (a+b)(a²−ab+b²)
Exam-style example
If x + 1/x = 5 (x ≠ 0), find x² + 1/x².
Square: 25 = x² + 2 + 1/x² → 23.
Remember: Squaring a sum introduces the middle term 2ab.
Avoid this mistake: (a+b)² is not a²+b².
16
Squares, Cubes & Indices
Must-remember formula
aᵐ × aⁿ = aᵐ⁺ⁿ
(aᵐ)ⁿ = aᵐⁿ
aᵐ/aⁿ = aᵐ⁻ⁿ (a ≠ 0)
√(a²) = |a| for real a
Exam-style example
Evaluate (2³ × 3²) ÷ 6.
(8 × 9)/6 = 12.
Remember: 35²: calculate 3 × 4 = 12 and append 25 → 1225.
Avoid this mistake: When taking √(a²), the answer is nonnegative |a|.
17
Ages
Must-remember formula
Elder = (Sum of ages + Difference)/2
Younger = (Sum of ages − Difference)/2
Future age = Present age + years
Exam-style example
Two people have combined age 46 years and differ by 8 years. Elder age?
(46 + 8)/2 = 27 years.
Remember: Ages increase together, so their difference stays constant.
Avoid this mistake: A ratio of ages can change over time, even though their difference does not.
Cover these based on your exam syllabus; the last two sections are optional for exams that exclude them.Part 4: Mixtures, Geometry, DI & Other Topics
18
Mixture & Alligation
Must-remember formula
Weighted average price = Total cost/Total quantity
Cheaper : Dearer = (Dearer − Mean):(Mean − Cheaper)
Exam-style example
Rice at ₹40/kg and ₹50/kg is mixed to cost ₹46/kg. Quantity ratio?
(50 − 46):(46 − 40) = 4:6 = 2:3.
Remember: Alligation: subtract diagonally.
Avoid this mistake: Make sure the desired mean is between the cheaper and dearer prices.
19
Partnership
Must-remember formula
Profit share ∝ Capital × Time
A:B profit = (A capital × A months):(B capital × B months)
Exam-style example
A invests ₹8,000 for 12 months, B ₹12,000 for 8 months. Profit ratio?
8000 × 12 : 12000 × 8 = 96000:96000 = 1:1.
Remember: Multiply amount and duration, then simplify.
Avoid this mistake: A larger investment does not guarantee a larger share if its duration is shorter.
20
Geometry & Plane Figures
Must-remember formula
Rectangle: area = l × b; perimeter = 2(l+b)
Circle: area = πr²; circumference = 2πr
Triangle: area = ½bh; angles sum to 180°
Right triangle: a²+b²=c²
Exam-style example
A right triangle has perpendicular sides of 9 cm and 12 cm. Hypotenuse?
√(9² + 12²) = √225 = 15 cm.
Remember: Know the triples 3-4-5, 5-12-13 and 8-15-17.
Avoid this mistake: Area uses cm²; perimeter uses cm.
21
Mensuration (3D)
Must-remember formula
Cuboid volume = lbh; total surface area = 2(lb+bh+hl)
Cylinder volume = πr²h; curved surface area = 2πrh
Sphere volume = (4/3)πr³; surface area = 4πr²
Cone volume = ⅓πr²h; curved surface area = πrl
Exam-style example
Cylinder radius 7 cm, height 10 cm. Curved surface area (π=22/7)?
2 × 22/7 × 7 × 10 = 440 cm².
Remember: Volume = cubic units; surface area = square units.
Avoid this mistake: For a cone, l is slant height, not vertical height.
22
Data Interpretation
Must-remember formula
Percentage growth = (New−Old)/Old × 100
Share of total = Part/Total × 100
Average = Total/Number of observations
Exam-style example
A depot moves 240 containers last year and 360 this year. Growth %?
(360−240)/240 × 100 = 50%.
Remember: Read the units, then find only the two needed values.
Avoid this mistake: Always divide by the old/base value when finding percentage increase.
23
Probability
Must-remember formula
Probability = Favourable outcomes/Total equally likely outcomes
0 ≤ Probability ≤ 1
Complement rule: P(not A) = 1−P(A)
Exam-style example
What is the chance of an even result on a fair six-sided die?
Even results = 2, 4, 6 → 3/6 = 1/2.
Remember: Count outcomes carefully before dividing.
Avoid this mistake: The simple ratio formula assumes equally likely outcomes.
24
Permutation & Combination
Must-remember formula
nPr = n!/(n−r)!
nCr = n!/[r!(n−r)!]
n! = n(n−1)…1, and 0! = 1
Exam-style example
In how many ways can 2 students be chosen from 5?
⁵C₂ = 5×4/(2×1) = 10 ways.
Remember: Arrangement → permutation; selection → combination.
Avoid this mistake: Order does not matter when choosing an unordered group.
25
Basic Trigonometry
Must-remember formula
sin θ = Opposite/Hypotenuse
cos θ = Adjacent/Hypotenuse
tan θ = Opposite/Adjacent
sin²θ + cos²θ = 1
Exam-style example
In a right triangle, opposite = 3 and hypotenuse = 5. Find sin θ.
sin θ = 3/5 = 0.6.
Remember: SOH–CAH–TOA helps remember the ratios.
Avoid this mistake: tan 90° is undefined; only revise trig if it is in your exam syllabus.
60-Second Final Formula Sheet
Read this compact sheet twice, then cover it and try recalling each formula from memory.
PercentagePart/Total × 100
Successive changea+b+ab/100
Profit %Profit/CP × 100
Discount %Discount/MP × 100
Simple interestPRT/100
CI amountP(1+R/100)ⁿ
AverageSum/Count
Work rate1/Time
SpeedDistance/Time
Train + platform(Train+Platform)/Speed
Still-water speed(D+U)/2
Stream speed(D−U)/2
PartnershipCapital × Time
HCF & LCMProduct = HCF × LCM (two integers)
Circle areaπr²
Cylinder volumeπr²h
5-Question Recall Challenge
Try each question without looking above. Tap “Reveal” only after answering. These are original practice questions.
Q1. A value rises by 20% and then falls by 20%. Find the net change.
A. No change
B. 4% decrease
C. 4% increase
D. 2% decrease
Reveal correct answer & shortcut
B. 4% decrease — Use 20²/100 = 4% loss.
Q2. A and B finish the same job in 10 and 15 days individually. Together?
A. 5 days
B. 6 days
C. 8 days
D. 12 days
Reveal correct answer & shortcut
B. 6 days — Time = (10×15)/(10+15) = 6 days.
Q3. An article is bought for ₹500 and sold for ₹625. Find profit %.
A. 20%
B. 22%
C. 25%
D. 30%
Reveal correct answer & shortcut
C. 25% — Profit = ₹125; 125/500×100 = 25%.
Q4. A 150 m train crosses a pole in 10 s. Find the speed.
A. 45 km/h
B. 54 km/h
C. 60 km/h
D. 72 km/h
Reveal correct answer & shortcut
B. 54 km/h — 150/10 = 15 m/s; multiply by 18/5 to get 54 km/h.
Q5. Find the difference between CI and SI on ₹10,000 at 10% for 2 years (annual compounding).
A. ₹50
B. ₹100
C. ₹150
D. ₹200
Reveal correct answer & shortcut
B. ₹100 — Difference = 10,000×(10/100)² = ₹100.
How to Revise This in 30 Minutes
00–05 min · Calculation toolkitFractions, squares, roots and unit conversions.
05–15 min · ArithmeticPercentage, ratio, average, P&L, interest.
15–25 min · Work, speed, numbersWork rates, trains, HCF/LCM, algebra.
25–30 min · Recall quizAnswer the five mixed questions and inspect your mistakes.
This 30-minute timetable is for candidates who already know the basics. Adjust it if your exam places extra emphasis on geometry, data interpretation or other topics.
FAQs: Last-Minute Maths Formula Revision
Which Maths formulas are most useful for SSC and RRB exams?
Start with percentage, ratio, average, profit and loss, interest, number system, time and work, speed, algebra and mensuration. Check your particular exam syllabus for weightage.
Can I revise competitive Maths in 30 minutes?
Yes, if you already know the basics: spend 5 minutes on conversions, 10 on arithmetic, 10 on work/speed/numbers and 5 on missed mock-test questions.
Does this sheet include actual previous-year questions?
No. It contains original exam-style examples and commonly practised formula types. It does not claim to reproduce official previous-year questions.
What is the fastest way to remember formulas?
Use active recall: read the formula, close the page, say it aloud, then solve one example without checking the solution.
Which Maths chapters should I prioritize for CONCOR?
Prioritize the quantitative aptitude topics named in the official syllabus for your specific CONCOR post. This sheet is wider than any single exam syllabus.
Should I memorize every formula in this article?
No. Master the high-frequency arithmetic formulas first, then use your syllabus and mock-test mistakes to decide what needs more attention.
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