NCERT MATHS Class 7 Chapter 7 Comparing Quantities Exercise 7.1, Q-5, 6, 7, 8, 9 and 10

Class 7 Maths – Chapter 7: Comparing Quantities (Introduction in Detail)

In our daily life, we often compare two quantities to understand which is more, less, equal, or how much one quantity differs from another. This process of comparison is called Comparing Quantities. In this chapter, we learn different mathematical methods to compare quantities using ratios, percentages, profit and loss, discount, and simple interest.


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1. Comparison of Quantities

When we compare two quantities of the same kind, we use ratio.

Ratio

A ratio shows how many times one quantity is greater or smaller than another.

Example:
If there are 20 boys and 10 girls in a class,
Ratio of boys to girls = 20 : 10 = 2 : 1


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2. Percentage

A percentage means “per hundred” and is represented by the symbol %.

1% = 1 out of 100

Percentages help us compare quantities easily.


Conversion

Fraction → Percentage: Multiply by 100

Percentage → Fraction: Divide by 100


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


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3. Increase and Decrease in Percentage

Percentage is used to find how much a quantity has increased or decreased.

Formula

Percentage increase =


\frac{\text{Increase}}{\text{Original value}} \times 100

\frac{\text{Decrease}}{\text{Original value}} \times 100

Example:
If price increases from ₹100 to ₹120,
Increase = ₹20
Percentage increase = (20/100) × 100 = 20%


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4. Profit and Loss

When we buy and sell goods, we calculate profit or loss.

Cost Price (CP): Price at which an article is bought

Selling Price (SP): Price at which an article is sold


Conditions

If SP greater than CP → Profit

If SP less than CP → Loss


Formulas

Profit = SP – CP

Loss = CP – SP



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5. Discount

A discount is the reduction given on the marked price of an article.

Marked Price (MP): Price written on the article

Discount = MP – SP


Discount Percentage

\frac{\text{Discount}}{\text{Marked Price}} \times 100


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6. Simple Interest

Simple Interest (SI) is the extra money paid for using someone’s money.

Terms

Principal (P): Money borrowed

Rate (R): Rate of interest per year

Time (T): Time period


Formula

SI = \frac{P \times R \times T}{100}


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Importance of Comparing Quantities

Helps in shopping and budgeting

Useful in business (profit, loss, discount)

Important in banks and loans (interest)

Makes real-life calculations easier



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Conclusion

Chapter 7 Comparing Quantities teaches us how to compare numbers using percentages, ratios, profit and loss, discount, and interest. These concepts are very important for everyday life and help students develop practical mathematical skills.


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