Aptitude Exam Formula Sheet with Examples
1. Arithmetic / Number Problems
Percentages
Percentage = (Part/Whole) × 100
Example: 45 out of 60 passed → 45/60×100=75%
Part = (Percentage × Whole)/100
Example: 20% of 150 → 20×150/100=30
Whole = (Part × 100)/Percentage
Example: 30 is 25% → 30×100/25=120
% Increase = (New−Old)/Old ×100
Example: 200→250 → (250−200)/200×100=25%
% Decrease = (Old−New)/Old ×100
Example: 150→120 → (150−120)/150×100=20%
Profit & Loss
Profit = SP − CP
Example: CP=500, SP=600 → Profit=100
Loss = CP − SP
Example: CP=600, SP=500 → Loss=100
Profit % = (Profit/CP)×100 → 100/500×100=20%
Loss % = (Loss/CP)×100 → 100/600×100≈16.67%
SP = CP + Profit → 500+100=600
SP = CP − Loss → 600−100=500
Simple Interest
SI = (P×R×T)/100
Example: P=10,000, R=5%, T=2 → SI=1,000
Amount = P + SI → 10,000 +1,000=11,000
Average
Average = Sum of terms / Number of terms
Example: 60,70,80 → (60+70+80)/3=70
Ratio & Proportion
Ratio = A:B
To divide X in ratio a:b → Part1=a/(a+b)×X, Part2=b/(a+b)×X
Example: 120 in 2:4 → Part1=40, Part2=80
2. Speed, Distance & Time
Speed = Distance / Time
Example: 150 km / 3 hr = 50 km/h
Time = Distance / Speed
Example: 120 km / 60 km/h = 2 hr
Distance = Speed × Time
Example: 60 km/h × 2 hr = 120 km
Relative Speed (same direction) = V1 − V2
Example: 60−40=20 km/h
Relative Speed (opposite direction) = V1 + V2
Example: 60+40=100 km/h
3. Time & Work
Work = Rate × Time
Example: A completes in 10 days → Rate=1/10 job/day
Combined Work = 1/x + 1/y → Days = 1/(1/x + 1/y)
Example: A=10d, B=15d → 1/10+1/15=1/6 → 6 days together
4. Algebra
Linear: ax + b = c → x = (c−b)/a
Example: 3x+6=18 → x=4
Quadratic: ax² + bx + c=0 → x= (-b ± √(b²−4ac))/2a
Example: x²−5x+6=0 → x=2,3
Difference of squares: a²−b²=(a+b)(a−b)
Example: 25−9=(5+3)(5−3)=16
Square of sum: (a+b)²=a²+2ab+b²
Example: (3+2)²=9+12+4=25
Square of difference: (a−b)²=a²−2ab+b²
Example: (5−3)²=25−30+9=4
5. Geometry & Mensuration
Triangle: Area = ½ × base × height
Example: b=10, h=5 → Area=25 Rectangle: Area = l×b, Perimeter=2(l+b)
Example: l=8,b=5 → Area=40, Perimeter=26 Square: Area=a², Perimeter=4a
Example: a=6 → Area=36, Perimeter=24 Circle: Area=πr², Circumference=2πr
Example: r=7 → Area≈153.86, Circumference≈43.96 Trapezium: Area=½(a+b)×height
Example: a=8,b=6,h=4 → Area=28 Parallelogram: Area=base×height
Example: b=10,h=5 → Area=50 Cube: Volume=a³, SA=6a²
Example: a=4 → V=64, SA=96 Cuboid: Volume=l×b×h, SA=2(lb+bh+hl)
Example: l=5,b=3,h=2 → V=30, SA=62 Cylinder: Volume=πr²h, SA=2πr(h+r)
Example: r=3,h=7 → V≈197.82, SA≈188.4 Sphere: Volume=4/3πr³, SA=4πr²
Example: r=3 → V≈113.1, SA≈113.1 Cone: Volume=1/3πr²h, SA=πr(l+r), l=√(r²+h²)
Example: r=3,h=4 → l=5 → V≈37.7, SA≈75.4
6. Probability
P = Favorable / Total
Example: Roll a die → P(get 3)=1/6
7. Miscellaneous / Shortcuts
Simple Interest Shortcut (1 year) = P×R/100
Example: 10,000×5/100=500
Combined Work Rate = sum of individual rates × Time
Example: A=1/10, B=1/15 → Together rate 1/6
Relative speed formulas already included above
End of Formula Sheet
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