Class 7 Mathematics

Chapter 8: Comparing Quantities

                                        

STAGE 0: Foundation

In daily life, we often compare quantities such as price, weight, marks, profit, and loss. This chapter helps us understand comparison using ratios, percentages, profit & loss.

Examples:

• Discount offers in shops
• Profit or loss in business
• Increase or decrease in prices

STAGE 1: Ratio

A ratio compares two quantities of the same kind.

Example:
Ratio of 3 apples to 5 apples = 3 : 5

Ratios should always be written in their simplest form.

STAGE 2: Percentage

Percentage means "per hundred".

Formula:

Percentage = (Part ÷ Whole) × 100

Example:

If a student scores 40 marks out of 50:

Step 1: Write the fraction = 40/50
Step 2: Convert into percentage = (40 ÷ 50) × 100
Step 3: Simplify = 80%

✅ Answer: 80%

STAGE 3: Profit and Loss

• Cost Price (CP): Price at which an item is bought
• Selling Price (SP): Price at which an item is sold

Profit: When SP > CP

Loss: When CP > SP

Profit Formula:
Profit = SP − CP

Loss Formula:
Loss = CP − SP

STAGE 4: Profit Percentage

Formula:

Profit % = (Profit ÷ CP) × 100

Example:

CP = ₹200, SP = ₹240

Step 1: Profit = 240 − 200 = 40
Step 2: Profit % = (40 ÷ 200) × 100
Step 3: Simplify = 20%

✅ Answer: 20% profit

STAGE 5: Loss Percentage

Formula:

Loss % = (Loss ÷ CP) × 100

Example:

CP = ₹500, SP = ₹450

Step 1: Loss = 500 − 450 = 50
Step 2: Loss % = (50 ÷ 500) × 100
Step 3: Simplify = 10%

✅ Answer: 10% loss

STAGE 6: Increase and Decrease Percentage

Increase % Formula:

Increase % = (Increase ÷ Original value) × 100

Decrease % Formula:

Decrease % = (Decrease ÷ Original value) × 100

Example:

Price increases from ₹100 to ₹120.

Step 1: Increase = 120 − 100 = 20
Step 2: Increase % = (20 ÷ 100) × 100 = 20%

✅ Answer: 20% increase

STAGE 7: Practice Questions

1. Find 25% of 200.
2. A pen is bought for ₹50 and sold for ₹60. Find the profit percentage.
3. Find the loss % if CP = ₹400 and SP = ₹360.
4. The price of a shirt is increased from ₹800 to ₹880. Find the increase percentage.
5. Write the formula for percentage.

---

Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 8: Comparing Quantities

⬅️ Back to Class 7 Maths Library