Class 8 Mathematics – Comparing Quantities

1. Introduction

• Comparing quantities means analyzing how one quantity relates to another.

• Useful in daily life, business, and finance.

• Main methods include percentage, profit/loss, and interest calculations.

2. Percentage

• Percentage expresses a number as a part of 100.

• Helps to compare quantities of different scales easily.

• Applications:

  • Discounts in shopping

  • Exam scores

  • Population statistics

  • Increase or decrease in prices

Key Concept:

• Percentages allow us to normalize values for easy comparison.

3. Profit and Loss

• Profit: When selling price > cost price → gain.

• Loss: When selling price < cost price → loss.

Applications:

• Buying and selling in shops

• Business transactions

• Understanding financial health

Key Concepts:

• Profit and loss are always calculated relative to cost price.

• Knowing profit/loss helps in deciding selling price or evaluating transactions.

4. Interest (Simple and Compound)

• Interest is the extra money paid or earned on principal money over time.

1. Simple Interest (SI):

   • Interest calculated only on the original principal.

   • Useful for short-term loans or investments.

2. Compound Interest (CI):

   • Interest calculated on principal + previously earned interest.

   • Useful for long-term investments, savings, and bank deposits.

Key Concepts:

• Interest reflects the cost of borrowing or benefit of investing.

• Compound interest grows faster than simple interest over time.

5. Practical Tips for Comparing Quantities

1. Use percentage to compare quantities of different magnitudes.

2. Profit/loss should be analyzed in terms of cost price.

3. Interest helps to compare savings or loans over time.

4. Always check increase or decrease relative to original quantity.

6. Key Points to Remember

• Percentage: Part of 100; used to compare easily.

• Profit/Loss: Compare selling price with cost price to evaluate transactions.

• Interest: Simple or compound; reflects cost or gain over time.

• Helps in real-life calculations like shopping, banking, and finance.