Class 7 Notes - Comparing Quantities

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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

  1. Express 3:5 as a percentage.
  2. If a book costs ₹120 and is sold for ₹150, find the profit percent.
  3. Find the simple interest on ₹2000 at 6% per annum for 3 years.
  4. If a shirt’s price is reduced from ₹500 to ₹400, what is the percentage decrease?
  5. 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.