Simply CBSE

Chapter 8 - Percentage and its Applications — Class 7 Mathematics

Quick revision guide with key points, definitions, and formulas for Percentage

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📌 Key Points

  • Percentage means 'per hundred'. It expresses a part as a fraction of 100.
  • Symbol: % (percent). Example: 25% means 25 out of 100.
  • 25% = 25/100 = 1/4. Always simplify the fraction.
  • To convert % to decimal: Divide by 100. 25% = 0.25
  • To convert decimal to %: Multiply by 100. 0.5 = 50%
  • To convert fraction to %: Multiply by 100. 1/2 = 50%
  • Percentage of = (Percentage/100) × Quantity. Formula: P = (p/100) × q
  • Profit = Selling Price - Cost Price (when SP > CP)
  • Loss = Cost Price - Selling Price (when CP > SP)
  • Profit% = (Profit/Cost Price) × 100. Always divide by CP, not SP.
  • Loss% = (Loss/Cost Price) × 100. Always divide by CP, not SP.
  • Discount = Marked Price - Selling Price. Discount% = (Discount/MP) × 100
  • Simple Interest = (Principal × Rate × Time) / 100. SI = (P × R × T) / 100
  • Amount = Principal + Simple Interest. Total amount = P + SI
  • Tax = (Tax%/100) × Original Price. Final Price = Original + Tax

📘 Important Definitions

Percentage
A number expressed as a fraction of 100. Symbol %. Example: 50% = 50/100 = 1/2
Profit
The gain when selling price is more than cost price. Profit = SP - CP
Loss
The loss when cost price is more than selling price. Loss = CP - SP
Discount
Reduction in the marked price of an item. Usually given as percentage.
Simple Interest
Interest calculated on principal only for a fixed period. SI = (P×R×T)/100
Principal
The original amount of money lent or borrowed. Amount on which SI is calculated.
Rate
The percentage at which interest is charged per annum (yearly).
Tax
A percentage-based charge added to the price of goods/services. Example: GST.

🔢 Formulas & Laws

Percentage

Percentage = (Part / Whole) × 100

To find what percent one quantity is of another

Percentage of

Percentage of = (P/100) × Quantity

To find a percentage of a given quantity

Profit and Loss

Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100

Always calculate on cost price (CP)

Discount

Discount% = (Discount/MP) × 100; SP = MP - Discount

Calculate on marked price (MP)

Simple Interest

SI = (P × R × T) / 100; Amount = P + SI

P = Principal, R = Rate (% p.a.), T = Time (years)

⚠️ Common Mistakes

✗ Wrong: 20% of 50 = 20 × 50 = 1000

✓ Correct: Correct: 20% of 50 = (20/100) × 50 = 10, NOT 1000

✗ Wrong: Profit% = (Profit/SP) × 100

✓ Correct: Correct: Profit% = (Profit/CP) × 100. Divide by cost price, not selling price.

✗ Wrong: Discount% = (Discount/SP) × 100

✓ Correct: Correct: Discount% = (Discount/MP) × 100. Divide by marked price, not SP.

✗ Wrong: SI = P × R × T (forgetting to divide by 100)

✓ Correct: Correct: SI = (P × R × T) / 100. Must divide by 100.

✗ Wrong: Final Price = Original - Tax

✓ Correct: Correct: Final Price = Original + Tax. Tax is added, not subtracted.

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Finding percentage of a quantity
1m★★★
Percentage-based word problems (profit/loss, discount)
2m★★★
Discount and marked price calculations
2m★★
Simple interest calculations
2m★★
Conversion between percentage, fraction, and decimal
1m★★★
Tax and final price calculations
2m

🎯 Last-Minute Recall

Close your eyes and try to recall: Key definitions, formulas, and 3 common mistakes. If you can recall 80% without looking, you're exam-ready!