Class 8 Comparing Quantities: NCERT Practice Questions

Mathematics becomes more practical and relatable when we start applying it to real-life situations. One such important chapter in Class 8 is Comparing Quantities. Whether it’s calculating discounts while shopping, understanding profit and loss in business, or dealing with interest in banks—this chapter forms the foundation of many everyday calculations.

In this blog, we will clearly explain all the key concepts from the NCERT Class 8 chapter “Comparing Quantities” in a simple and student-friendly way. The content is aligned with the NCERT level and syllabus to ensure clarity and relevance.

Important note:
This blog is purely for concept understanding and practice. You will find plenty of practice questions at the end, but no solutions are provided, so students can test their understanding effectively.

What is Comparing Quantities?

Comparing quantities means understanding how one quantity relates to another. Instead of just finding differences, we often express comparisons in terms of:

• Ratios

• Percentages

• Profit and Loss

• Discounts

• Interest

This helps us make better decisions in real life for example, choosing the best deal while shopping.

Ratio and Percentage

Ratio

A ratio compares two quantities of the same kind.

Example:
If there are 20 boys and 30 girls in a class, the ratio of boys to girls is:
20 : 30 = 2 : 3

Percentage

Percentage means “per hundred”.

Example:
If 50 out of 100 students passed, then:
Percentage = 50%

Conversion Between Fraction and Percentage

• Fraction → Percentage: Multiply by 100

• Percentage → Fraction: Divide by 100

Example:
1/2 = 50%
25% = 25/100 = 1/4

Finding Increase or Decrease Percentage

Percentage Increase

Used when a value increases.

Formula:
Increase % = (Increase / Original Value) × 100

Percentage Decrease

Used when a value decreases.

Formula:
Decrease % = (Decrease / Original Value) × 100

Real-Life Example

If the price of a product increases from ₹100 to ₹120:
Increase = ₹20
Percentage Increase = (20/100) × 100 = 20%

Profit and Loss

This is one of the most important topics in this chapter.

Key Terms

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

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

Profit

When SP > CP
Profit = SP − CP

Profit % = (Profit / CP) × 100

Loss

When SP < CP
Loss = CP − SP

Loss % = (Loss / CP) × 100

Example

If CP = ₹500 and SP = ₹550:
Profit = ₹50
Profit % = (50/500) × 100 = 10%

Discount

When a shopkeeper reduces the marked price, it is called a discount.

Terms

• Marked Price (MP): Original price of the product

• Discount: Reduction in price

• Selling Price (SP): Final price after discount

Formula

Discount = MP − SP

Discount % = (Discount / MP) × 100

Example

If MP = ₹1000 and discount = 20%:
Discount = ₹200
SP = ₹800

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Simple Interest (SI)

Interest is the extra money paid when we borrow money.

Formula

SI = (P × R × T) / 100

Where:

• P = Principal

• R = Rate of interest

• T = Time

Example

If P = ₹1000, R = 5%, T = 2 years:
SI = (1000 × 5 × 2) / 100 = ₹100

Compound Interest (CI)

In compound interest, interest is calculated on both the principal and the previous interest.

Key Idea

Interest is added to the principal after each time period.

Formula (Basic)

Amount = P × (1 + R/100)^T

CI = Amount − Principal

Example

If P = ₹1000, R = 10%, T = 2 years:
Amount = 1000 × (1.1)^2 = ₹1210
CI = ₹210

Difference Between Simple Interest and Compound Interest

Applications of Comparing Quantities

This chapter is widely used in:

• Shopping (discounts)

• Business (profit/loss)

• Banking (interest)

• Data interpretation

• Budget planning

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Practice Questions (NCERT Level)

Section 1: Basic Percentage

1. Convert the following into percentages:
   a) 3/5
   b) 7/20
   c) 0.25

2. Convert the following percentages into fractions:
   a) 45%
   b) 12.5%
   c) 80%

3. Find the percentage of:
   a) 25 out of 200
   b) 18 out of 60
   c) 72 out of 90

Section 2: Increase and Decrease

4. A number increases from 80 to 100. Find the percentage increase.

5. The price of a shirt decreases from ₹500 to ₹400. Find the percentage decrease.

6. Population of a town increased from 20,000 to 25,000. Find the percentage increase.

Section 3: Profit and Loss

7. A shopkeeper buys an article for ₹250 and sells it for ₹300. Find the profit and profit percentage.

8. A man sells a bicycle for ₹1800 at a loss of ₹200. Find the cost price.

9. Find the loss percentage when CP = ₹600 and SP = ₹540.

10. A trader gains ₹120 on selling an article. If CP = ₹800, find the gain percentage.

Section 4: Discount

11. A shopkeeper gives a discount of 10% on a product marked at ₹1000. Find the selling price.

12. A dress marked at ₹1500 is sold for ₹1200. Find the discount and discount percentage.

13. A shop offers 25% discount on a bag costing ₹800. Find the final price.

Section 5: Simple Interest

14. Find the simple interest on ₹2000 at 5% per annum for 3 years.

15. Calculate the amount when ₹1500 is invested at 4% per annum for 2 years (simple interest).

16. Find the rate of interest if ₹1000 becomes ₹1100 in 2 years (SI).

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Section 6: Compound Interest

17. Find the compound interest on ₹1000 for 2 years at 10% per annum.

18. Calculate the amount for ₹2000 invested for 3 years at 5% per annum (compounded annually).

19. Find the difference between simple interest and compound interest on ₹1000 for 2 years at 10%.

Section 7: Mixed Application Questions

20. A shopkeeper marks his goods 20% above the cost price and gives a discount of 10%. Find his profit percentage.

21. A sum of money doubles in 5 years at simple interest. Find the rate of interest.

22. A man bought a TV for ₹20,000 and sold it at a loss of 10%. Find the selling price.

23. The population of a city increases by 10% annually. Find the population after 2 years if the current population is 50,000.

Section 8: Higher Thinking Questions

24. If the price of an item is increased by 20% and then decreased by 20%, is the final price equal to the original price?

25. A trader gives two successive discounts of 10% and 20%. Find the total discount percentage.

26. A sum of money amounts to ₹1210 in 2 years at 10% per annum compound interest. Find the principal.

Applications of Percentage in Daily Life (Class 8 Comparing Quantities)

Percentages are not just a mathematical concept—they are used almost everywhere in daily life. From shopping malls to bank statements, percentages help us make smart decisions. In Class 8, understanding how percentages apply in real situations is very important.

For example, when you see a “Flat 30% Off” sign in a store, you are using percentage to calculate how much money you will save. Similarly, when exam results are declared, your performance is often expressed in percentage.

Banks also use percentages to calculate interest on savings or loans. Even population growth, tax calculations, and data comparisons are based on percentages.

Key areas where percentages are used:

• Shopping discounts

• Exam results

• Banking and finance

• Business profits

• Data comparison

Understanding these applications helps students connect mathematics with real life, making the subject more interesting and meaningful.

Successive Changes and Their Effect (Class 8 Comparing Quantities)

In many real-life situations, a value does not change just once—it changes multiple times. This is called successive increase or decrease.

For example, the price of an item may increase by 10% one year and again by 20% the next year. Similarly, discounts may be applied more than once.

Important concept:
Successive percentage changes are not simply added or subtracted.

Example idea:

• Increase by 10% and then 20% ≠ 30% total increase

• Decrease by 20% and then increase by 20% does not bring back the original value

This happens because the base value changes after each step.

This topic is important because it:

• Improves logical thinking

• Helps avoid common mistakes

• Prepares students for higher-level maths

Understanding Taxes and Bills (Class 8 Comparing Quantities)

Another practical application of comparing quantities is in understanding taxes and bills.

When you buy something, especially in real life, the price you pay is often higher than the marked price due to taxes like GST (Goods and Services Tax). These taxes are calculated as a percentage of the price.

For example:

• If GST is 18%, it means you pay an extra 18% on the original price

• Final amount = Original price + tax

Similarly, electricity bills, mobile bills, and online purchases often include additional charges calculated using percentages.

Learning this concept helps students:

• Understand real bills

• Avoid confusion while shopping

• Make better financial decisions

Tips to Solve Comparing Quantities Questions (Class 8 Level)

To score well in this chapter, students need a clear strategy while solving questions. Many mistakes happen not because the concept is wrong, but because of confusion in steps.

Here are some useful tips:

1. Identify the Type of Question

First, check whether the question is about:

• Profit and loss

• Discount

• Interest

• Percentage change

This helps in selecting the correct formula.

2. Write Given Values Clearly

Always note down:

• CP, SP, MP

• Principal, Rate, Time

• Increase or decrease

This avoids confusion later.

3. Use the Correct Formula

Each concept has its own formula. Do not mix them up.

4. Be Careful with Percentage Calculations

Convert percentages properly:

• 20% = 20/100

• 5% = 5/100

5. Practice Regularly

The more you practice, the better you understand patterns in questions.

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Conclusion

The chapter Comparing Quantities (Class 8) is not just about formulas—it is about understanding how numbers behave in real life. From calculating discounts during sales to understanding bank interest, this chapter builds essential life skills.

To master this topic:

• Practice regularly

• Understand formulas instead of memorizing blindly

• Solve real-life problems

• Attempt the practice questions given above without looking at solutions

With consistent practice, you will find this chapter not only easy but also highly useful in daily life.