Comparing Quantities - Class 7 Mathematics (CBSE)
Based on the 2025-26 NCERT syllabus for Class 7 Mathematics. This chapter extends the concepts of ratio, proportion, and percentage to practical applications including profit-loss and simple interest.
1. Why this chapter matters
Comparing quantities is one of the most practical chapters in Class 7 mathematics. It is used in shopping discounts, bank interest, exam percentages, business profit calculations, and data analysis. In CBSE exams, this chapter contributes 10-12 marks with a strong emphasis on word problems.
2. Ratio
A ratio compares two quantities of the same kind.
- Written as a:b or a/b.
- Ratio has no unit.
- Quantities must be in the same unit before comparing.
Simplifying ratios
Divide both terms by their highest common factor (HCF). Ratio 12:18 simplifies to 2:3 (dividing by 6).
Equivalent ratios
Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio. 2:3 = 4:6 = 6:9 = 8:12.
3. Proportion
When two ratios are equal, they are in proportion.
a:b = c:d means a, b, c, d are in proportion. Written as a:b :: c:d.
Product of extremes = product of means
In a proportion a:b = c:d:
- a and d are extremes.
- b and c are means.
- a x d = b x c.
Unitary method
Find the value of one unit first, then multiply to find the required quantity.
Example: 5 pens cost Rs. 75. Cost of 8 pens = (75/5) x 8 = 15 x 8 = Rs. 120.
4. Percentage
Percentage means 'per hundred' or 'out of 100.'
Converting fraction to percentage
Multiply the fraction by 100. 3/5 = (3/5) x 100 = 60 percent.
Converting decimal to percentage
Multiply by 100. 0.45 = 0.45 x 100 = 45 percent.
Converting percentage to fraction
Divide by 100 and simplify. 65 percent = 65/100 = 13/20.
Converting percentage to decimal
Divide by 100. 32 percent = 32/100 = 0.32.
5. Profit and loss
Key terms
- Cost Price (CP): The price at which an item is bought.
- Selling Price (SP): The price at which an item is sold.
- Profit: SP - CP (when SP > CP).
- Loss: CP - SP (when CP > SP).
- Overhead expenses: Additional costs (transport, repair) added to CP.
Formulas
Profit = SP - CP. Loss = CP - SP. Profit percentage = (Profit / CP) x 100. Loss percentage = (Loss / CP) x 100.
Important notes
Profit and loss percentages are ALWAYS calculated on the cost price, not on the selling price.
6. Simple interest
When money is borrowed, the borrower pays extra money called interest.
Key terms
- Principal (P): The borrowed amount.
- Rate (R): Interest percentage per year.
- Time (T): Duration in years.
- Amount (A): Principal + Interest.
Formula
Simple Interest (SI) = (P x R x T) / 100. Amount = P + SI.
Example
If Rs. 5000 is borrowed at 8 percent per annum for 3 years: SI = (5000 x 8 x 3) / 100 = Rs. 1200. Amount = 5000 + 1200 = Rs. 6200.
7. Worked examples
Example 1: Find 20 percent of Rs. 450.
20 percent of 450 = (20/100) x 450 = 90. Answer = Rs. 90.
Example 2: A shopkeeper bought a chair for Rs. 400 and sold it for Rs. 480. Find profit percentage.
Profit = 480 - 400 = Rs. 80. Profit percentage = (80/400) x 100 = 20 percent.
Example 3: Find simple interest on Rs. 8000 at 6 percent per annum for 2.5 years.
SI = (8000 x 6 x 2.5) / 100 = (8000 x 6 x 5) / (100 x 2) = 240000/200 = Rs. 1200.
Example 4: In a class of 50 students, 60 percent are boys. How many are girls?
Boys = 60 percent of 50 = (60/100) x 50 = 30. Girls = 50 - 30 = 20.
8. Common mistakes and how to fix them
| Mistake | Fix |
|---|---|
| Calculating profit/loss % on SP | Always calculate on CP |
| Forgetting to convert years and months | Convert time fully into years (6 months = 0.5 years) |
| Mixing up ratio and proportion order | a:b :: c:d means a/b = c/d |
| Ignoring overhead expenses | Add overhead expenses to the cost price |
| Wrong unit in ratio comparison | Convert both quantities to same unit first |
9. CBSE exam focus
| Question type | Marks | Frequency |
|---|---|---|
| Ratio and proportion | 2-3 marks | 1 question |
| Percentage conversion and calculation | 2 marks | 1 question |
| Profit and loss | 3 marks | 1 question |
| Simple interest | 3 marks | 1 question |
| Mixed word problems | 4 marks | Occasional |
10. Self-test
- Express 45 percent as a fraction in lowest terms.
- Find 15 percent of Rs. 600.
- A laptop is bought for Rs. 25,000 and sold for Rs. 22,500. Find the loss percentage.
- Find the simple interest on Rs. 10,000 at 7.5 percent per annum for 4 years.
- The ratio of boys to girls in a school is 3:2. If there are 600 boys, how many girls are there?
- A dealer sold a TV for Rs. 18,000, gaining 20 percent. Find the cost price.
11. Answer key
- 45/100 = 9/20.
- (15/100) x 600 = Rs. 90.
- Loss = 25000 - 22500 = Rs. 2500. Loss percent = (2500/25000) x 100 = 10 percent.
- SI = (10000 x 7.5 x 4) / 100 = Rs. 3000.
- Ratio 3:2 means 3 parts = 600. Each part = 200. Girls = 2 x 200 = 400.
- Let CP = x. SP = x + 20 percent of x = 1.20x. 1.20x = 18000. x = 18000/1.20 = Rs. 15000.
12. Quick revision
- Ratio compares quantities. Proportion equates ratios.
- Percentage means out of 100.
- Profit/Loss percent always on CP.
- Simple Interest = (P x R x T) / 100.
- Amount = Principal + Interest.
- Unitary method: find value of one, then multiply.
