1. Consider these pairs: 5% of 40 and 40% of 5; 25% of 12 and 12% of 25; 15% of 60 and 60% of 15. What general statement best describes what you notice?

2. A school is organising an excursion for its students. 40% of them are Grade 8 students and the rest are Grade 9 students. Among the Grade 8 students, 60% are girls. What percentage of the students going to the excursion are Grade 8 girls?

3. A school is organising an excursion for its students. 40% of them are Grade 8 students and the rest are Grade 9 students. Among the Grade 8 students, 60% are girls. If the total number of students going to the excursion is 160, how many of them are Grade 8 girls?

4. A shopkeeper sells pencils at a price such that the selling price of 3 pencils is equal to the cost of 5 pencils. Does he make a profit or a loss, and what is the percentage?

5. The bus fares were increased by 3% last year and by 4% this year. What is the overall percentage increase in the last 2 years?

6. If the length of a rectangle is increased by 10% and the area remains unchanged, by what percentage (exactly) does the breadth decrease?

7. Three shops sell the same items at the same price. The shops offer deals as follows: Shop A: “Buy 1 and get 1 free”; Shop B: “Buy 2 and get 1 free”; Shop C: “Buy 3 and get 1 free”. If the price of one item is ₹100, which arrangement from cheapest to costliest correctly lists the effective price per item?

8. Suppose you need 4 items. Which shop’s deal is the most cost-effective?

9. In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 98%?