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General Aptitude Formula Cheat Sheet — All 17 Topics

Complete formula reference covering all 17 General Aptitude topics with shortcuts and tips. Bookmark for quick revision before placement tests, competitive exams, and aptitude rounds.

Percentages

  • Percentage = (Value / Total) × 100
  • New Value = Original × (100 ± P) / 100
  • For increase: multiply by (100 + P)/100. For decrease: multiply by (100 - P)/100
  • Discount = Marked Price - Selling Price
  • Successive change: Net% = a + b + (a × b)/100
  • Fraction equivalents: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
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Profit & Loss

  • Profit = Selling Price - Cost Price
  • Profit % = (Profit / CP) × 100
  • Loss = Cost Price - Selling Price
  • Loss % = (Loss / CP) × 100
  • SP = CP × (100 + Profit%) / 100
  • SP = CP × (100 - Loss%) / 100
  • False weight profit% = (Error / Actual) × 100
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Ratio & Proportion

  • a:b = a/b — ratio compares two quantities
  • If a:b = x:y, then a = kx, b = ky (multiplier method)
  • Proportion: a:b :: c:d means a/b = c/d, cross multiply: ad = bc
  • Sum of parts = (a+b)x, Difference = |a-b|x
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Time & Work

  • Work = Time × Rate (Rate = efficiency)
  • If person takes T days: Rate = 1/T work per day
  • Combined Rate = Rate₁ + Rate₂ + ... (add rates, NOT times)
  • LCM method: Total Work = LCM of individual times
  • Pipe problems: Inlet = +ve rate, Outlet = -ve rate
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Time-Speed-Distance

  • Speed = Distance / Time, Distance = Speed × Time, Time = Distance / Speed
  • km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5
  • Avg Speed = Total Distance / Total Time (NOT average of speeds)
  • Equal distances: Avg = (2 × S₁ × S₂) / (S₁ + S₂)
  • Relative: Towards → add speeds. Same direction → subtract speeds
  • Train + Platform: Distance = Train length + Platform length
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Simple & Compound Interest

  • SI = (P × R × T) / 100
  • Amount = P + SI
  • CI: Amount = P × (1 + R/100)^T
  • CI = Amount - P
  • Difference CI - SI for 2 years = P × (R/100)²
  • Half-yearly compounding: Use R/200 and 2T periods
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Averages

  • Average = Sum of values / Number of values
  • Sum = Average × Number of values
  • Missing value = (Average × N) - Sum of known values
  • Weighted Avg = (W₁V₁ + W₂V₂ + ...) / (W₁ + W₂ + ...)
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Number Series

  • Arithmetic progression: Tn = a + (n-1)d, Sum = n/2[2a + (n-1)d]
  • Geometric progression: Tn = a × r^(n-1)
  • Check differences first, then ratios, then squares/cubes
  • Alternating series: check even/odd position patterns separately
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Mixtures & Alligations

  • Concentration = (Solute / Solution) × 100
  • Alligation rule: (Q₁/Q₂) = (C₂ - Cm) / (Cm - C₁)
  • Replacement: Final = Original × (1 - x/V)^n
  • Mean price method for mixing two items
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Permutations & Combinations

  • n! = n × (n-1) × (n-2) × ... × 1
  • Permutations: nPr = n! / (n-r)!
  • Combinations: nCr = n! / [r!(n-r)!]
  • nC₀ = nCn = 1, nC₁ = n, nCr = nC(n-r)
  • Arrangement with repetitions: n^r
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Probability

  • P(Event) = Favorable outcomes / Total possible outcomes
  • For coins: Total outcomes = 2^n. For dice: Total outcomes = 6^n
  • Independent events: P(A and B) = P(A) × P(B)
  • Mutually exclusive: P(A or B) = P(A) + P(B)
  • Not mutually exclusive: P(A or B) = P(A) + P(B) - P(A and B)
  • P(not A) = 1 - P(A)
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Algebraic Equations

  • (a+b)² = a² + 2ab + b²
  • (a-b)² = a² - 2ab + b²
  • a² - b² = (a+b)(a-b)
  • Linear: ax + b = c → x = (c-b)/a
  • Two variables: solve by substitution or elimination
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Quadratic Problems

  • ax² + bx + c = 0
  • Roots: x = [-b ± sqrt(b²-4ac)] / 2a
  • Sum of roots = -b/a, Product of roots = c/a
  • Discriminant: D = b² - 4ac (D>0 real, D=0 equal, D<0 complex)
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Geometry Basics

  • Circle: Area = πr², Circumference = 2πr
  • Triangle: Area = 1/2 × base × height
  • Right triangle: a² + b² = c² (Pythagoras)
  • Equilateral triangle: Area = (√3/4) × side²
  • Rectangle: Area = l × w, Perimeter = 2(l + w)
  • Square: Area = side², Perimeter = 4 × side
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Data Interpretation

  • Percentage share = (Part / Whole) × 100
  • Growth rate = [(New - Old) / Old] × 100
  • Average of values = Total / Number of items
  • Inferred total from a percentage share = Value / (Percentage/100)
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Logical Puzzles

  • Draw constraints as a board or table first
  • Apply each clue one at a time, eliminating impossible cases
  • Ranking: draw horizontal positions (left to right)
  • Syllogisms: use Venn diagrams or rules of inference
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Multi-Step Word Problems

  • Break into sub-problems: Part 1 → Result 1 → Part 2 → Result 2
  • Define all variables before writing equations
  • Check units match across all steps
  • Validate final answer against original question
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