CBSE Notes Class 8 Maths Chapter 7 Comparing Quantities

Chapter 7 of CBSE Class 8 Mathematics introduces students to the practical world of calculations involving ratios, percentages, and financial concepts. This chapter bridges the gap between theoretical mathematics and real-world applications, helping students understand everyday financial transactions better.

1.0CBSE Class 8 Maths Chapter 7 Comparing Quantities - Revision Notes

1. Core Concepts and Their Applications

(a) Fractions, Ratios, and Percentages

• Fractions represent parts of a whole (like 1/4, 3/5)
• Ratios compare quantities (for example, 3 : 5 means for every 3 units of one item, there are 5 of another)
• Percentages express parts per hundred (50% means 50 parts per 100)

(b) Percentage Changes

• Increase calculation: New Value = Original + (Original × Percentage increase)
• Decrease calculation: New Value = Original - (Original × Percentage decrease)

Example: A mobile phone costs Rs 15,000. With a 5% increase: 15,000 + (15,000 × 5/100) = Rs 15,750 With 5% decrease: 15,000 - (15,000 × 5/100) = Rs 14,250

2. Commercial Mathematics

(a) Discount Calculations Basic Formula: Discount = Marked Price - Sale Price Percentage Discount: Discount = (Discount% × Marked Price)/100

Example Box:

Market Price: Rs. 535

Sale Price: Rs. 495

Discount = Rs 535 - Rs 495 = Rs 40

(b) Profit and Loss

• Profit = Selling Price - Cost Price
• Profit% = (\frac{Profit\ Cost}{ Price}) × 100
• Loss = Cost Price - Selling Price
• Loss% = (\frac{Loss}{Cost\ Price}) × 100

3. Interest Calculations

(a) Simple Interest (SI) Formula: $SI=\frac{(Principal\times Rate\times Time)}{100}$

(b) Compound Interest (CI) Formula:

$Amount=Principal(1+\frac{Rate}{100}{)}^{time}andCI=Amount-Principal$

Important Note: For half-yearly compounding:

• Use R/2 as rate
• Use 2n as time period

4. Tax Calculations

Sales Tax/VAT Formula:

• Tax Amount = (Tax% × Selling Price)/100
• Final Price = Selling Price + Tax Amount

Example:

Watch Price: Rs. 1,200

VAT = 8%

Tax Amount = (8/100 x 1,200) = Rs 96

Final Price = Rs 1,200 + Rs 96 = Rs 1,296

5. Practical Applications

Population Growth:

• Uses the compound interest principle
• Growth = Current Population(1 + Growth Rate/100)^years

Example: 

Initial Population: 3,26,40,000 

Growth Rate: 2% annually 

After 2 years = 3,26,40,000(1 + 2/100)² = 3,39,58,656

2.0Solved Examples of CBSE Maths Notes for Class 8 Chapter 7 Comparing Quantities

Example 1: A number is increased by 20%, and then it is decreased by 20%. Find the net increase or decrease percent.

Solution: Let the number be 100 

Increase in the number = 20% of 100 = 20 

So Increased number = 100 + 20 = 120

Decrease in the number = 20% of 120 = 20/100 ×120 = 24 

So, new number = 120 – 24 = 96 

Net decrease = 100 – 96 = 4 

Hence, net decrease per cent = 4 100 ×100 = 4%

Example 2: Vishakha offers a discount of 20% on all the items at her shop and still makes a profit of 12%. What is the cost price of an article marked at Rs 280?

Solution: Marked Price = Rs 280 

Discount = 20% of Rs 280 = (20/100) x  280 = Rs 56 

So selling price = Rs (280 – 56) = Rs 224 

Let the cost price be Rs 100 

Profit = 12% of Rs 100 = Rs 12 

So selling price = Rs (100 + 12) = Rs 112 

If the selling price is Rs 112, cost price = Rs 100 

If the selling price is Rs 224, cost price = Rs 100/224 x 112 = Rs 200.

Example 3: Find the compound interest on Rs 48,000 for one year at 8% per annum when compounded half yearly.

Solution: Principal (P) = Rs 48,000 

Rate (R) = 8% p.a., Time (n) = 1 year 

Interest is compounded half-yearly  

$A=P(1+\frac{R}{200}{)}^{2n}$

$A=48000(1+\frac{8}{200}{)}^2$

= 48000 x 26/25 x 26/25     

= 76.8 × 26 × 26 = Rs 51,916.80 

Therefore, Compound Interest = A – P 

= Rs (519,16.80 – 48,000) 

= Rs 3,916.80

3.0Key Features of CBSE Maths Notes for Class 8 Chapter 7 Comparing Quantities

• CBSE Maths Notes for Class 8 Chapter 7 - Comparing Quantities are designed to cover real-world applications, including shopping calculations, banking transactions, population studies, and business calculations.
• The notes also emphasise step-by-step problem-solving, providing clear working methods, detailed solutions, and multiple approaches to solving problems when applicable.
• Additionally, the notes include a visual learning component, such as a quick reference chart that outlines the formulas for calculating increases, decreases, profit percentages, and loss percentages.
• The notes also provide memory tips, such as the understanding that compound interest (CI) always gives more interest than simple interest (SI), the relationship between selling price (SP) and cost price (CP) in determining profit or loss, and the formula for calculating the final price after a discount (Final Price = Marked Price - Discount).