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.
1.0Download CBSE Class 8 Maths Chapter 7 Comparing Quantities Notes : Free PDF
Download the free PDF of CBSE Class 8 Maths Chapter 7 Comparing Quantities Notes to master topics like percentages, ratios, profit and loss, and simple and compound interest. These notes are concise, easy to follow, and perfect for quick revision.
2.0CBSE Class 8 Maths Chapter 7 Comparing Quantities - Revision Notes
- Core Concepts and Their Applications
(a) Fractions, Ratios, and Percentages
- The 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
- 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% = (PriceProfit Cost)×100
- Loss = Cost Price - Selling Price
- Loss% = (Cost PriceLoss)×100
- Interest Calculations
(a) Simple Interest (SI) Formula: SI=100(Principal×Rate×Time)
(b) Compound Interest (CI) Formula:
Amount=Principal(1+100Rate)timeandCI=Amount−Principal
Important Note: For half-yearly compounding:
- Use R/2 as rate
- Use 2n as time period
- 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
- 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
3.0Solved 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+200R)2n
A=48000(1+2008)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
4.0Key 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).