Percentages (Copy)

Percentage Calculations Cheat Sheet

1. Calculate a Given Percentage of a Quantity

• Formula:
  (Percentage ÷ 100) × Quantity
• Example:
  Find 25% of 200 → (25 ÷ 100) × 200 = 50

2. Express One Quantity as a Percentage of Another

• Formula:
  (Part ÷ Whole) × 100
• Example:
  Express 30 as a percentage of 120 → (30 ÷ 120) × 100 = 25%

3. Calculate Percentage Increase or Decrease

• Formula:
  ((New Value – Original Value) ÷ Original Value) × 100
• If answer is positive → Increase
• If answer is negative → Decrease
• Example:
  Original price = 80, New price = 100
  % Change = ((100 – 80) ÷ 80) × 100 = 25% Increase

4. Calculate with Simple and Compound Interest (Formulas Not Given)

• Simple Interest (SI):
  SI = (Principal × Rate × Time) ÷ 100
• Example:
  ₨1000 at 5% p.a. for 3 years → (1000 × 5 × 3) ÷ 100 = ₨150
• Compound Interest (CI):
  CI = Total Amount – Principal
  Total Amount = Principal × (1 + Rate/100)ⁿ
  (n = number of years)
• Example:
  ₨1000 at 10% p.a. for 2 years
  Total = 1000 × (1.10)² = ₨1210 → CI = 1210 – 1000 = ₨210

Common Percentage Calculations

• Deposit:
  Deposit = (Deposit % × Total Price) ÷ 100
• Example: 10% deposit on ₨5000 → (10 × 5000) ÷ 100 = ₨500

• Discount:
  Discount = (Discount % × Original Price) ÷ 100
  Selling Price = Original Price – Discount
• Example: 20% discount on ₨1500 → (20 × 1500) ÷ 100 = ₨300
  Selling Price = 1500 – 300 = ₨1200

• Profit and Loss:
  • Profit/Loss Amount = Selling Price – Cost Price
  • Profit/Loss % = (Profit or Loss ÷ Cost Price) × 100
• Example:
  Cost Price = ₨200, Selling Price = ₨250
  Profit = 250 – 200 = ₨50
  Profit % = (50 ÷ 200) × 100 = 25%

• Earnings (e.g., Commission, Bonus):
  Earnings = (Percentage Rate × Total Sales) ÷ 100
• Example:
  5% commission on ₨40,000 sales → (5 × 40,000) ÷ 100 = ₨2000

• Percentages Over 100:
  When percentage exceeds 100%, calculate normally.
• Example:
  Find 120% of 250 → (120 ÷ 100) × 250 = 300

Quick Reference Values

• 50% = Half
• 25% = Quarter
• 10% = One-Tenth
• 1% = Divide by 100
• 200% = Double
• 150% = One and a Half Times

Reverse Percentage (Finding Original Value)

• Formula:
  Original Value = Final Value ÷ (1 ± (Percentage ÷ 100))
• Use ‘+’ for increase, ‘−’ for decrease
• Example:
  After 20% decrease, price = ₨80
  Original = 80 ÷ 0.80 = ₨100

Successive Percentage Changes

• Apply percentages step by step.
• Example:
  Increase ₨200 by 10%, then by 20%
  First: 200 + 20 = 220
  Then: 220 + 44 = 264

Conversion Tips

• Fraction to Percentage: (Fraction × 100)
• Decimal to Percentage: (Decimal × 100)
• Percentage to Decimal: Divide by 100

Examples:
0.75 = 75%
3/5 = 60%
125% = 1.25

Handling Percentage Change in Profit/Loss

• New Value = Original Value × (1 ± (Percentage ÷ 100))
• Example:
  ₨500 increased by 15% → 500 × 1.15 = ₨575
  ₨500 decreased by 15% → 500 × 0.85 = ₨425