Comparing Quantities

We compare quantities every day using ratios and percentages, whether we are checking marks in a test, the rise in the price of milk or the discount offered in a sale. In this chapter you will revise ratios and percentages and use them to find percentage increase and decrease. You will learn the meaning of marked price, discount and selling price, and calculate discount percent. You will find profit and loss as a percentage of the cost price, including overhead expenses such as transport and repairs, and calculate sales tax or GST that is added to the bill. The second half deals with interest. You will compare simple interest with compound interest, where interest is added to the principal at the end of each conversion period. Using the formula A = P(1 + R/100)^n, you will find amounts compounded annually and half-yearly, and apply the same idea to the growth of populations and bacteria and the depreciation of machines and vehicles.

Detailed Worksheet: Comparing Quantities Section A - Definitions (10 marks) 1. Define ratio and percentage. Express the ratio 3 : 5 as a percentage. (2 marks) 2. Define marked price, discount and discount percent. On which price is discount always calculated? (2 marks) 3. What are overhead expenses? How are they treated when finding the cost price of an article? (2 marks) 4. What is GST? Why is it calculated on the selling price and not on the cost price? (2 marks) 5. Define principal, amount and conversion period. Distinguish between simple interest and compound interest. (2 marks) Section B - Calculations and Applications (15 marks) 6. A shirt is marked at Rs 1,200 and is sold at a discount of 15%. GST of 12% is charged on the reduced price. Find the discount, the sale price and the final bill amount. (3 marks) 7. A dealer buys a television for Rs 18,000 and spends Rs 2,000 on its transport. He sells it for Rs 22,000. Find his profit or loss percent. (3 marks) 8. Find the compound interest on Rs 10,000 for 2 years at 10% per annum compounded annually. How much more is it than the simple interest for the same period? (3 marks) 9. The population of a town is 25,000. It increases at the rate of 4% per annum. Find the population after 2 years. (3 marks) 10. Find the compound interest on Rs 8,000 for 1 year at 10% per annum compounded half-yearly. (3 marks) Section C - Diagrams (10 marks) 11. Draw a flow diagram showing how the final bill is obtained for a jacket marked at Rs 2,000, sold at a discount of 10% with 18% GST charged on the sale price. Write the amount at each step of the diagram. (4 marks) 12. In a class of 40 students, 16 like cricket, 10 like football and the rest like other games. Express each group as a percentage and draw a percentage bar 10 cm long, divided into three labelled parts. (3 marks) 13. Draw a time line from Year 0 to Year 3 showing how Rs 5,000 grows at 10% per annum compound interest. Mark the amount at the end of each year. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Shop P offers a discount of 20% on a cycle marked at Rs 5,000. Shop Q offers two successive discounts of 10% and 10% on the same cycle. Find the price at each shop, decide which offer is better, and explain why two successive discounts of 10% are not the same as one discount of 20%. (5 marks) 15. A machine is bought for Rs 1,50,000. Its value depreciates at 10% per annum. Find its value after 2 years and after 3 years. Explain how the formula for depreciation is related to the formula for compound interest. (5 marks) 16. Ramesh sold two cycles for Rs 3,000 each. On one he gained 20% and on the other he lost 20%. Find the cost price of each cycle and his overall gain or loss percent. A classmate says that there is no gain and no loss. Explain why this is wrong. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Show all working, write the formula used and give money answers in rupees.