📚 Formula Sheet for Competitive Exams
🧮 Percentage
Percentage = (Value / Total) × 100
Increase/Decrease % = (Difference / Original) × 100
Percentage point change = New Percentage - Old Percentage
🚶 Speed, Time, Distance
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
Average Speed = Total Distance / Total Time
Convert km/hr to m/s: Multiply by (5/18)
Convert m/s to km/hr: Multiply by (18/5)
💰 Simple Interest
SI = (P × R × T) ÷ 100
Amount (A) = P + SI
P = Principal, R = Rate (per annum), T = Time in years
💱 Compound Interest
Amount (A) = P × (1 + R/100)
T
CI = A - P = P × [(1 + R/100)
T
- 1]
When interest is compounded Half-yearly: Rate = R/2, Time = 2T
When interest is compounded Quarterly: Rate = R/4, Time = 4T
📐 Area & Volume
Area of Square = side²
Perimeter of Square = 4 × side
Area of Rectangle = length × width
Perimeter of Rectangle = 2 × (length + width)
Area of Circle = πr²
Circumference of Circle = 2πr or πd
Area of Triangle = ½ × base × height
Volume of Cube = side³
Surface Area of Cube = 6 × side²
Volume of Cuboid = length × width × height
Volume of Cylinder = πr²h
Curved Surface Area of Cylinder = 2πrh
Total Surface Area of Cylinder = 2πr(h + r)
📊 Average
Average = Sum of observations ÷ Number of observations
Weighted Average = (w₁x₁ + w₂x₂ + ...) / (w₁ + w₂ + ...)
📈 Profit & Loss
Profit = Selling Price (SP) - Cost Price (CP)
Loss = Cost Price (CP) - Selling Price (SP)
Profit % = (Profit / CP) × 100
Loss % = (Loss / CP) × 100
SP = CP × (100 + Profit%) / 100
SP = CP × (100 - Loss%) / 100
Discount = Marked Price - Selling Price
Discount % = (Discount / Marked Price) × 100
👷 Time & Work
If A does a work in 'n' days, A's 1-day work = 1/n
(A + B)'s 1-day work = 1/n + 1/m (if A takes n days, B takes m days)
Work = Men × Days (M₁D₁ = M₂D₂)
Work = Men × Days × Hours (M₁D₁H₁ = M₂D₂H₂)
🔢 Ratio & Proportion
Ratio a:b = a/b
Product of Means = Product of Extremes (a:b :: c:d ⇒ bc = ad)
Compounded Ratio of (a:b) and (c:d) is (ac:bd)
Duplicate Ratio of a:b is a²:b²
Sub-duplicate Ratio of a:b is √a:√b
🧮 HCF & LCM
Product of two numbers = HCF × LCM
HCF of Fractions = HCF of Numerators / LCM of Denominators
LCM of Fractions = LCM of Numerators / HCF of Denominators