Comparing Quantities
In this chapter, students learn how to compare different quantities using ratios, percentages, and proportions. These concepts are essential for understanding real-life situations like shopping discounts, profit and loss, interest calculations, and more.
1. Ratio
- A ratio compares two quantities of the same kind by division.
- It is written as a : b or a/b.
- Example: If there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
2. Proportion
- Proportion states that two ratios are equal.
- It is written as a : b :: c : d or a/b = c/d.
- Example: 2:3 :: 4:6 (because 2/3 = 4/6)
3. Percentage
- A percentage is a fraction with denominator 100.
- It is denoted by the symbol %.
- Example: 25% means 25 out of 100.
- To convert a fraction to percentage: multiply by 100.
Example: 3/4 × 100 = 75% - To convert a percentage to fraction: divide by 100.
Example: 60% = 60/100 = 3/5
4. Increase and Decrease Percent
- To find percentage increase: (Increase ÷ Original value) × 100
- To find percentage decrease: (Decrease ÷ Original value) × 100
- Example: If a shirt’s price increases from ₹200 to ₹250, increase = ₹50.
Percentage increase = (50/200) × 100 = 25%
5. Profit and Loss
- Profit = Selling Price (SP) – Cost Price (CP)
- Loss = Cost Price (CP) – Selling Price (SP)
- Profit % = (Profit ÷ CP) × 100
- Loss % = (Loss ÷ CP) × 100
6. Simple Interest
- Simple Interest (SI) = (Principal × Rate × Time) ÷ 100
- Principal: The money borrowed or lent
- Rate: Interest rate per year
- Time: Number of years
- Example: ₹1000 at 5% per annum for 2 years
SI = (1000 × 5 × 2) ÷ 100 = ₹100
7. Real-life Applications
- Shopping discounts and offers
- Bank interest calculations
- Comparing marks, heights, weights, etc.
- Splitting bills and sharing costs
Practice Questions
- Express 3:5 as a percentage.
- If a book costs ₹120 and is sold for ₹150, find the profit percent.
- Find the simple interest on ₹2000 at 6% per annum for 3 years.
- If a shirt’s price is reduced from ₹500 to ₹400, what is the percentage decrease?
- Are the ratios 4:9 and 8:18 in proportion?
Summary
- Ratios, proportions, and percentages help compare quantities.
- Profit, loss, and interest are practical applications of these concepts.
- Understanding these ideas is useful in daily life, especially in shopping and banking.