Quantitative Aptitude Formulas 2025
Master placement exams with our comprehensive collection of quantitative aptitude formulas. Essential formulas, shortcuts, and examples for TCS, Infosys, Wipro, and all major campus placements.
1. Percentage Formulas
| Formula | Explanation |
|---|---|
| Percentage = (Part/Whole) × 100 | Basic percentage calculation |
| x% of y = (x/100) × y = y% of x | Percentage is commutative |
| % Increase = [(New - Old)/Old] × 100 | Calculate percentage increase |
| % Decrease = [(Old - New)/Old] × 100 | Calculate percentage decrease |
| Net % Change = a + b + (ab/100) | Successive change of a% then b% |
Quick Shortcuts
- • 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
- • 33.33% = 1/3, 16.66% = 1/6, 12.5% = 1/8, 11.11% = 1/9
- • To find 15% of a number: find 10% and add half of it
Example Problem
Q: A salary increased by 20% and then decreased by 20%. What is the net change?
A: Net change = 20 + (-20) + (20 × -20)/100 = 0 - 4 = -4% decrease
2. Profit & Loss Formulas
| Formula | Usage |
|---|---|
| Profit = SP - CP | When SP > CP |
| Loss = CP - SP | When CP > SP |
| Profit % = (Profit/CP) × 100 | Profit percentage on cost |
| Loss % = (Loss/CP) × 100 | Loss percentage on cost |
| SP = CP × (100 + Profit%)/100 | Find SP from CP and profit % |
| SP = CP × (100 - Loss%)/100 | Find SP from CP and loss % |
| CP = SP × 100/(100 + Profit%) | Find CP from SP and profit % |
| Discount = MP - SP | MP = Marked Price |
Key Terms
- CP (Cost Price): Price at which an article is bought
- SP (Selling Price): Price at which an article is sold
- MP (Marked Price): Price labeled on the article (before discount)
3. Ratio & Proportion
| Concept | Formula |
|---|---|
| Ratio | a:b = a/b |
| Proportion | a:b = c:d → a×d = b×c (cross multiply) |
| Componendo | If a/b = c/d then (a+b)/b = (c+d)/d |
| Dividendo | If a/b = c/d then (a-b)/b = (c-d)/d |
| Componendo-Dividendo | If a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d) |
| Mean Proportion | If a:b = b:c then b = √(a×c) |
Example Problem
Q: If A:B = 2:3 and B:C = 4:5, find A:B:C
A: Make B common: A:B = 8:12, B:C = 12:15 → A:B:C = 8:12:15
4. Time & Work Formulas
| Formula | Application |
|---|---|
| Work = Rate × Time | Basic work formula |
| Rate = 1/Time (to complete 1 unit) | Efficiency per unit time |
| Time = Work/Rate | Time to complete work |
| Combined Rate = 1/A + 1/B | A and B working together |
| Time Together = (A×B)/(A+B) | If A finishes in 'a' days, B in 'b' days |
| M₁D₁H₁/W₁ = M₂D₂H₂/W₂ | M=Men, D=Days, H=Hours, W=Work |
Shortcut Tips
- • Use LCM method for easier calculations
- • If A is 2x faster than B, A:B work rate = 2:1
- • More workers = Less time (inverse proportion)
Example
Q: A finishes in 10 days, B in 15 days. Together?
A: (10×15)/(10+15) = 150/25 = 6 days
5. Speed, Distance & Time
| Formula | Description |
|---|---|
| Distance = Speed × Time | Basic formula (D = S × T) |
| Speed = Distance/Time | Finding speed |
| Time = Distance/Speed | Finding time |
| Avg Speed = Total Distance/Total Time | For varying speeds |
| Avg Speed = 2ab/(a+b) | Same distance at speeds a and b |
| Relative Speed = (a+b) | Objects moving towards each other |
| Relative Speed = |a-b| | Objects moving same direction |
Unit Conversions
- • km/hr to m/s: Multiply by 5/18
- • m/s to km/hr: Multiply by 18/5
- • 1 hour = 3600 seconds
- • 1 km = 1000 meters
Train Problems
- • Time to pass pole = Length/Speed
- • Time to pass platform = (L₁+L₂)/Speed
- • Time for trains to cross = (L₁+L₂)/Relative Speed
6. Simple & Compound Interest
Simple Interest (SI)
SI = (P × R × T)/100
Amount = P + SI = P(1 + RT/100)
- • P = Principal (initial amount)
- • R = Rate of interest per annum
- • T = Time in years
Compound Interest (CI)
Amount = P(1 + R/100)ⁿ
CI = Amount - P
- • n = number of time periods
- • Half-yearly: n = 2T, R = R/2
- • Quarterly: n = 4T, R = R/4
Quick Comparison
Difference between CI and SI for 2 years:
CI - SI = P(R/100)² = PR²/10000
7. Algebra Essentials
Important Identities
Quadratic Equation: ax² + bx + c = 0
- x = (-b ± √(b² - 4ac)) / 2a
- • Sum of roots = -b/a
- • Product of roots = c/a
- • Discriminant (D) = b² - 4ac
- If D > 0: Two real roots | D = 0: One root | D < 0: No real roots
8. Geometry Formulas
2D Shapes
Rectangle
Area = l × b | Perimeter = 2(l + b)
Square
Area = a² | Perimeter = 4a | Diagonal = a√2
Circle
Area = πr² | Circumference = 2πr
Triangle
Area = ½ × base × height
Trapezium
Area = ½ × (a + b) × h
3D Shapes
Cube
Volume = a³ | Surface = 6a²
Cuboid
Volume = l×b×h | Surface = 2(lb+bh+hl)
Cylinder
Volume = πr²h | CSA = 2πrh
Cone
Volume = (1/3)πr²h | CSA = πrl
Sphere
Volume = (4/3)πr³ | Surface = 4πr²
Frequently Asked Questions
Which topics are most important for placement exams?
Percentage, Profit & Loss, Time & Work, and Speed-Distance-Time form the core of most aptitude tests. Master these first, then move to other topics. These topics typically account for 60-70% of questions.
How should I approach solving aptitude problems?
First, identify the topic and relevant formula. Then, check if any shortcuts apply. Practice mental math for simple calculations. Time yourself to improve speed. Always verify your answer if time permits.
How many questions can I expect in a placement exam?
Most placement exams (TCS, Infosys, Wipro) have 15-25 quantitative aptitude questions. Time limit is usually 1-2 minutes per question. Focus on accuracy first, then improve speed.
Should I memorize all formulas?
Yes, but with understanding. Memorize the basic formulas, but understand when to apply each. Practice enough problems that formulas become second nature. Don't just memorize—know why each formula works.
What's the best way to improve calculation speed?
Practice mental math daily. Learn tables up to 20, squares up to 30, and cubes up to 15. Master percentage-to-fraction conversions. Use approximation techniques for complex calculations.
How much time should I spend preparing for aptitude?
Dedicate 1-2 hours daily for 2-3 months before placements. Solve at least 10-15 problems per topic. Take weekly mock tests to track progress and identify weak areas.
Practice With Real Problems
Knowing formulas is just the first step. Practice with our free aptitude test tool to apply these formulas and improve your speed.