50 Most Important Quantitative Aptitude Formulas for SSC Exams (With Solved Examples)
Quantitative Aptitude is the most crucial, high-scoring section in staff selection examinations including SSC CGL, SSC CHSL, SSC CPO, SSC GD, and SSC MTS. In Tier 1 and Tier 2 stages, speed and accuracy in mathematical calculations decide the final cutoff merit rank.
While conceptual understanding is the foundation, memorizing standard formulas and rapid shortcut identities saves over 30 to 45 seconds per question in a live computer-based test (CBT).
In this master guide, our academic team has compiled the 50 most repeated Quantitative Aptitude formulas across Arithmetic and Advanced Mathematics, complete with mathematical definitions, shortcut tricks, and step-by-step solved examples.
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Table of Contents (Topics Covered)
📊 1. Percentage & Successive Changes (Formulas 1–6)
Formula 1: Basic Percentage Calculation
Percentage = (Part Value / Total Value) × 100%Formula 2: Percentage Increase / Decrease
% Change = (|Final Value - Initial Value| / Initial Value) × 100%Formula 3: Net Successive Percentage Change (2 Changes: a% & b%)
Net % Change = [a + b + (a × b / 100)]%Note: Use positive sign for increase/profit and negative sign for decrease/discount.
Formula 4: Price-Consumption-Expenditure Relation
If price increases by r%, then the reduction in consumption required to keep expenditure constant is:
% Reduction = [r / (100 + r)] × 100%Formula 5: If Price Decreases by r%
% Increase in Consumption = [r / (100 - r)] × 100%Formula 6: Population Growth / Machine Depreciation After n Years
Population after n years = P × (1 ± r/100)ⁿ💡 Solved Example (SSC CGL 2024 Question):
Question: If the price of sugar is increased by 25%, by what percentage must a household reduce its consumption so that total expenditure remains unchanged?
Solution: Here r = 25%.
Using Formula 4: Reduction = [25 / (100 + 25)] × 100 = (25 / 125) × 100 = 20%.
🏷️ 2. Profit, Loss & Discount (Formulas 7–12)
Formula 7: Profit % and Loss %
Profit % = [(SP - CP) / CP] × 100% | Loss % = [(CP - SP) / CP] × 100%Formula 8: Direct Selling Price Formula
SP = CP × [(100 ± Profit%/Loss%) / 100]Formula 9: Single Equivalent Discount for Successive Discounts (d₁% & d₂%)
Equivalent Discount % = [d₁ + d₂ - (d₁ × d₂ / 100)]%Formula 10: Relationship Between Marked Price (MP) and Cost Price (CP)
MP / CP = (100 + Profit%) / (100 - Discount%)Formula 11: Two Articles Sold at Same SP (One at x% Gain, Other at x% Loss)
Always Overall Loss % = (x / 10)² % = (x² / 100)%Formula 12: Dishonest Dealer Profit Percentage
Gain % = [Error / (True Value - Error)] × 100%💡 Solved Example (SSC CHSL PYQ):
Question: A shopkeeper marks an article 40% above cost price and allows a discount of 20%. Find his net profit percentage.
Solution: Let CP = 100. Then MP = 140.
SP = 140 × (1 - 20/100) = 140 × 0.8 = 112.
Profit % = 112 - 100 = 12%.
💰 3. Simple & Compound Interest (Formulas 13–18)
Formula 13: Simple Interest (SI)
SI = (P × R × T) / 100Formula 14: Compound Interest Amount (Annually Compounded)
Amount (A) = P × (1 + R/100)ᵀ | CI = A - PFormula 15: Difference Between CI and SI for 2 Years (Most Repeated in SSC)
Difference (D₂) = P × (R / 100)²Formula 16: Difference Between CI and SI for 3 Years
Difference (D₃) = P × (R / 100)² × [(300 + R) / 100]Formula 17: Half-Yearly Compounding
Rate becomes (R / 2)%, Time becomes (2T) periodsFormula 18: Sum Doubling in SI Rule
If a sum becomes N times in T years at simple interest, rate R is:
R = [(N - 1) × 100] / T⚖️ 4. Ratio, Proportion & Alligation (Formulas 19–24)
Formula 19: Mean Proportion of a and b
Mean Proportional = √(a × b)Formula 20: Third Proportion of a and b
Third Proportional (c) = b² / aFormula 21: Fourth Proportion of a, b, c
Fourth Proportional (d) = (b × c) / aFormula 22: Partnership Profit Sharing Ratio
Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)Formula 23: Alligation Rule for Combining Two Ingredients
(Quantity of Cheaper) / (Quantity of Dearer) = (Price of Dearer - Mean Price) / (Mean Price - Price of Cheaper)Formula 24: Repeated Removal & Replacement of Liquid (Milk/Water)
If x units of liquid are drawn from a container of C capacity and replaced by water n times:
Remaining Pure Liquid = Initial Pure Quantity × [1 - (x / C)]ⁿ🚆 5. Time, Speed, Distance & Boats (Formulas 25–30)
Formula 25: Unit Conversion (km/h ↔ m/s)
1 km/h = 5/18 m/s | 1 m/s = 18/5 km/hFormula 26: Average Speed for Equal Distances (at speeds u & v)
Average Speed = (2 × u × v) / (u + v)Formula 27: Relative Speed (Opposite and Same Directions)
Opposite Directions = u + v | Same Direction = |u - v|Formula 28: Train Crossing a Platform/Bridge of Length L
Time = (Train Length + Platform Length) / Train SpeedFormula 29: Downstream & Upstream Boat Speeds
Downstream (D) = u + v | Upstream (U) = u - vFormula 30: Speed of Boat in Still Water (u) and Stream Speed (v)
Boat Speed (u) = (D + U) / 2 | Stream Speed (v) = (D - U) / 2⚙️ 6. Time, Work & Pipes/Cisterns (Formulas 31–35)
Formula 31: Combined Work of A & B (in x and y days)
Time Together = (x × y) / (x + y) daysFormula 32: MDH Formula for Men, Days, Hours and Work
(M₁ × D₁ × H₁ × E₁) / W₁ = (M₂ × D₂ × H₂ × E₂) / W₂Formula 33: Efficiency and Time Relation
Time ∝ 1 / Efficiency (If Efficiency Ratio is a:b, Time Ratio is b:a)Formula 34: Wages Division Rule
Wages are divided strictly in the ratio of Total Work Done = (Efficiency × Days Worked)Formula 35: Net Filling Rate with Leak/Inlet
Net Rate = (1 / Inlet Time) - (1 / Leak Time)🔢 7. Number System & Divisibility (Formulas 36–40)
Formula 36: Fundamental Division Theorem
Dividend = (Divisor × Quotient) + RemainderFormula 37: Sum of First n Natural Numbers
Sum = [n(n + 1)] / 2Formula 38: Sum of Squares of First n Natural Numbers
Sum = [n(n + 1)(2n + 1)] / 6Formula 39: Sum of Cubes of First n Natural Numbers
Sum = [n(n + 1) / 2]²Formula 40: Product of Two Numbers Rule
Number₁ × Number₂ = LCM(Number₁, Number₂) × HCF(Number₁, Number₂)📐 8. Algebra & Algebraic Identities (Formulas 41–44)
Formula 41: Standard SSC Power Shortcuts
If x + (1/x) = k → x² + (1/x²) = k² - 2
If x + (1/x) = k → x³ + (1/x³) = k³ - 3kFormula 42: Minus Power Shortcuts
If x - (1/x) = k → x² + (1/x²) = k² + 2
If x - (1/x) = k → x³ - (1/x³) = k³ + 3kFormula 43: Master Cubic Identity
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)Special Rule: If (a + b + c) = 0, then a³ + b³ + c³ = 3abc.
Formula 44: Three-Variable Square Identity
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)📦 9. Geometry & Mensuration 2D/3D (Formulas 45–48)
Formula 45: Equilateral Triangle Area, Height & Inradius/Circumradius
Area = (√3 / 4)a² | Height = (√3 / 2)a
Inradius (r) = a / (2√3) | Circumradius (R) = a / √3Formula 46: Circle & Cylinder Formulas
Circle Area = πr² | Circumference = 2πr
Cylinder Volume = πr²h | CSA = 2πrh | TSA = 2πr(h + r)Formula 47: Cone & Sphere Formulas
Cone Volume = (1/3)πr²h | Slant height (l) = √(r² + h²)
Sphere Volume = (4/3)πr³ | Sphere Surface Area = 4πr²
Hemisphere Volume = (2/3)πr³ | Hemisphere TSA = 3πr²Formula 48: Circle Tangent Secant Theorem
If PT is tangent from P and PAB is secant → PT² = PA × PB📐 10. Trigonometry & Heights (Formulas 49–50)
Formula 49: Three Fundamental Trigonometric Identities
1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ (sec²θ - tan²θ = 1)
3. 1 + cot²θ = cosec²θ (cosec²θ - cot²θ = 1)Formula 50: Height & Distance Ratio Tricks (30°-60°-90° & 45°-45°-90°)
For 30°-60°-90°: Opposite to 30° : Opposite to 60° : Hypotenuse = 1 : √3 : 2
For 45°-45°-90°: Base : Perpendicular : Hypotenuse = 1 : 1 : √2Why Perfect Rank is the Best Platform for SSC Exam Preparation
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Frequently Asked Questions (FAQs)
Which math topics have the highest weightage in SSC CGL & CHSL?+
Arithmetic topics (Percentage, Profit & Loss, Ratio, Time & Work, Speed Distance) along with Advanced Math (Algebra, Geometry, Trigonometry, Mensuration) account for over 80% of all math questions in SSC exams.
How can I remember all Quantitative Aptitude formulas for SSC?+
Create a 1-page formula cheat sheet, dedicate 15 minutes every morning to revision, solve 5-10 practical problems for each formula, and attempt timed mock tests on Perfect Rank to test instant memory recall under pressure.
Why is Perfect Rank considered the best platform for SSC exam preparation?+
Perfect Rank provides an authentic TCS-like CBT exam interface, 100% free bilingual mock tests (English & Hindi), detailed step-by-step KaTeX mathematical explanations, sectional drills, and real-time accuracy and speed analytics.
What is the difference between CI and SI for 2 years formula?+
The difference for 2 years at a constant annual interest rate R% is: Difference (D₂) = P × (R / 100)², where P represents the Principal sum.
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