Class 8 Math Comparing Quantities Notes

Comparing Quantities – Class 8

Hi kids! This chapter is all about Comparing Quantities. We’ll learn how to use percentages, calculate profit and loss, and understand simple interest – all things we use in everyday life!

1. Percentage

A percentage is a way of expressing a number as a fraction of 100. The word “percent” means “out of 100”. We use the symbol %.

Example: 25% means 25 out of 100, or 25/100, which can be simplified to 1/4.

Converting Fractions to Percentages:

Multiply the fraction by 100.

Example: 1/2 = (1/2) * 100 = 50%

Converting Percentages to Fractions:

Divide the percentage by 100 and simplify.

Example: 75% = 75/100 = 3/4

Example: If a shirt costs Rs. 500 and is on sale for 20% off, the discount is (20/100) * 500 = Rs. 100. The sale price is Rs. 500 – Rs. 100 = Rs. 400.

2. Profit and Loss

These terms are used in business to describe whether money is gained or lost in a transaction.

Cost Price (CP): The price at which an item is bought.
Selling Price (SP): The price at which an item is sold.
Profit: SP > CP. Profit = SP – CP
Loss: SP < CP. Loss = CP – SP
Profit Percentage: (Profit / CP) * 100
Loss Percentage: (Loss / CP) * 100

Example: A shopkeeper buys a toy for Rs. 200 and sells it for Rs. 250. The profit is Rs. 250 – Rs. 200 = Rs. 50. The profit percentage is (50/200) * 100 = 25%.

3. Simple Interest

Simple interest is a method of calculating interest on a principal amount. It’s calculated only on the original principal.

Principal (P): The original amount of money.
Rate (R): The percentage of interest per year.
Time (T): The number of years.
Simple Interest (SI): (P * R * T) / 100
Amount (A): P + SI

Example: If you deposit Rs. 1000 in a bank at a simple interest rate of 5% per year for 3 years, the simple interest earned is (1000 * 5 * 3) / 100 = Rs. 150. The total amount after 3 years will be Rs. 1000 + Rs. 150 = Rs. 1150.

These concepts are essential for understanding financial transactions, business deals, and many other real-world situations.

Comparing Quantities Quiz – Application Problems

1. Discount: A shopkeeper offers a 20% discount on a dress marked at Rs. 1500. What is the sale price of the dress?

Rs. 1200

Discount amount = (20/100) * 1500 = Rs. 300. Sale price = 1500 – 300 = Rs. 1200.

2. Profit: A fruit seller buys 10 kg of apples for Rs. 400 and sells them for Rs. 50 per kg. What is the profit percentage?

25%

Cost Price (CP) = Rs. 400. Selling Price (SP) = 10 kg * Rs. 50/kg = Rs. 500. Profit = SP – CP = 500 – 400 = Rs. 100. Profit % = (Profit/CP) * 100 = (100/400) * 100 = 25%.

3. Simple Interest: Rohan deposits Rs. 5000 in a bank at a simple interest rate of 6% per annum for 2 years. How much interest will he earn?

Rs. 600

Simple Interest (SI) = (P * R * T) / 100 = (5000 * 6 * 2) / 100 = Rs. 600.

4. Percentage Increase: The population of a town increased from 20,000 to 25,000. What is the percentage increase in population?

25%

Increase in population = 25,000 – 20,000 = 5,000. Percentage increase = (Increase/Original Population) * 100 = (5000/20000) * 100 = 25%.

5. Loss: A shopkeeper sells a chair for Rs. 800, incurring a loss of 20%. What was the cost price of the chair?

Rs. 1000

Let CP be x. SP = CP – (Loss %) of CP. 800 = x – (20/100)x. 800 = (80/100)x. x = (800 * 100) / 80 = Rs. 1000.

6. Percentage Decrease: The price of a car decreased from Rs. 500,000 to Rs. 450,000. What is the percentage decrease in price?

10%

Decrease in price = 500,000 – 450,000 = 50,000. Percentage decrease = (Decrease/Original Price) * 100 = (50,000/500,000) * 100 = 10%.

7. Profit and Loss: A vendor buys 5 dozen bananas for Rs. 200. He sells each banana for Rs. 5. What is his profit or loss percentage?

50% profit

5 dozen bananas = 5 * 12 = 60 bananas. CP = Rs. 200. SP = 60 * Rs. 5 = Rs. 300. Profit = 300 – 200 = Rs. 100. Profit % = (100/200) * 100 = 50%.

8. Simple Interest Calculation: What principal amount will earn Rs. 900 as simple interest in 3 years at a rate of 5% per annum?

Rs. 6000

SI = (P * R * T) / 100. 900 = (P * 5 * 3) / 100. P = (900 * 100) / (5 * 3) = Rs. 6000.

9. Successive Discounts: A shop offers a 10% discount followed by a 20% discount. What is the equivalent single discount?

28%</div

Let the marked price be Rs. 100. After the first discount (10%), the price becomes Rs. 90. After the second discount (20% of Rs. 90), the price becomes Rs. 72. Total discount = 100 – 72 = Rs. 28. Equivalent discount percentage = (28/100) * 100 = 28%.

10. Commission: A salesperson receives a 5% commission on all sales. If they sell goods worth Rs. 20,000, what is their commission amount?

Rs. 1000

Commission = (5/100) * 20,000 = Rs. 1000.