Lesson: Comparing Quantities
Topic: Finding Increase or Decrease Per Cent
Class: VIII
Teacher: M. RajaRao, MSc, MEd
1. Hook Activity (5-7 mins)
Imagine you're buying your favorite snack, which normally costs ₹100.
- Shop A offers a 20% discount.
- Shop B increased the price to ₹120 last week, but is now offering a ₹20 discount.
Which shop gives you a better price today?
- Shop A: 20% of ₹100 is ₹20. So, the price is ₹100 - ₹20 = ₹80.
- Shop B: The price is ₹120. A ₹20 discount means the price is ₹120 - ₹20 = ₹100.
Shop A is the better deal! This shows why understanding percentages is more powerful than just looking at flat discount amounts.
2. I Do (10 mins) - Teacher Models
I will show you how to find the new price, just like in the textbook example.
Example 1: Price Increase
The price of a scooter was ₹34,000 last year. It has increased by 20%. What is the new price?
Method 1: Find the increase amount first.
Increase = 20% of ₹34,000
= 20100 × 34,000 = ₹6,800
New Price = Old Price + Increase
= ₹34,000 + ₹6,800 = ₹40,800
Method 2: Unitary Method (Find the new percentage).
A 20% increase means the new price is 100% + 20% = 120% of the old price.
New Price = 120100 × 34,000 = ₹40,800
Example 2: Price Decrease
Suppose the scooter's price of ₹34,000 was decreased by 5% for a sale. What is the sale price?
Method 1: Find the decrease amount (reduction).
Reduction = 5% of ₹34,000
= 5100 × 34,000 = ₹1,700
New Price = Old Price - Reduction
= ₹34,000 - ₹1,700 = ₹32,300
3. We Do (10 mins) - Guided Practice
Let's solve one together. A T-shirt's price was ₹500. It's on sale for 15% off. Let's find the sale price.
(Calculate: 15% of ₹500)
(Calculate: ₹500 - Discount Amount)
4. You Do (10 mins) - Independent Practice
Try these problems on your own. Click the "Show Solution" button to check your work.
Problem 1
The population of a town was 50,000. In one year, it increased by 8%. What is the new population?
Click to see the solution
Increase in population: 8% of 50,000
= 8100 × 50,000 = 4,000
New Population: Old Population + Increase
= 50,000 + 4,000 = 54,000
Problem 2
A laptop originally costing ₹60,000 is available at a 10% discount. What is its new price?
Click to see the solution
Discount amount: 10% of ₹60,000
= 10100 × 60,000 = ₹6,000
New Price: Old Price - Discount
= ₹60,000 - ₹6,000 = ₹54,000
5. Conclusion (3-5 mins)
Today, we learned how to calculate the new value after a percentage increase or decrease. This is a very useful skill for shopping, understanding news about the economy, and more!
Key Takeaways:
- For a % Increase: New Value = Old Value + Increase Amount
- For a % Decrease: New Value = Old Value - Decrease Amount
6. Self-Assessment (3-5 mins)
How confident do you feel about these topics now? (Click 'Yes' or 'No')
1. I can explain what a 'percentage increase' means.
2. I can find the new price after a 20% discount.
3. I can calculate the new population after a 5% increase.