Comparing Quantities

We compare quantities all the time, such as marks in tests, prices of goods or the growth of savings. In this chapter you will revise ratios and learn that two ratios are in proportion when they are equal. You will then study percentage, which means "per hundred" and is written as %. You will convert fractions and decimals into percentages and back, for example 3/4 = 75% and 0.08 = 8%, find a percentage of a quantity, and express one quantity as a percentage of another. Percentages also describe an increase or decrease, such as a rise in price or a fall in population. The chapter applies percentages to buying and selling. When the selling price is more than the cost price there is a profit, and when it is less there is a loss; profit or loss percent is always calculated on the cost price. Finally, you will learn about simple interest, using SI = (P x R x T)/100 and amount = principal + interest.

Detailed Worksheet: Comparing Quantities Section A - Definitions (10 marks) 1. What is a percentage? Write 45 per hundred as a percentage and as a fraction in lowest terms. (2 marks) 2. Define cost price, selling price, profit and loss. (2 marks) 3. Write the formulas for profit percent and loss percent. Why are they calculated on the cost price? (2 marks) 4. Define principal, rate of interest, time period and amount. (2 marks) 5. Write the formula for simple interest and explain each term. (2 marks) Section B - Calculations and Applications (15 marks) 6. Convert: (i) 3/8 into a percentage (ii) 0.65 into a percentage (iii) 2.5 into a percentage (iv) 35% into a fraction in lowest terms (v) 4% into a decimal (vi) 120% into a mixed fraction. (3 marks) 7. Find: (i) 25% of 120 (ii) 12.5% of 640 (iii) 150% of 80. What percent of 75 is 15? (3 marks) 8. A shopkeeper buys a chair for Rs 375 and sells it for Rs 400. Another chair bought for Rs 500 is sold for Rs 460. Find the profit or loss percent in each case. (3 marks) 9. Find the simple interest and the amount on (i) Rs 10,000 at 5% per year for 3 years (ii) Rs 3,500 at 7% per year for 2 years. (3 marks) 10. The population of a town increased from 25,000 to 27,500 in one year. Find the percentage increase. If it decreased instead from 25,000 to 24,000, find the percentage decrease. (3 marks) Section C - Diagrams (10 marks) 11. Draw a 10 x 10 grid and shade 35% of it in one colour and 20% in another. Write the shaded parts as fractions and decimals, and find the percentage that is unshaded. (4 marks) 12. Draw a pie-type circle or bar showing the distribution of a family's monthly income of Rs 40,000: food 30%, rent 25%, education 15%, savings 20% and others 10%. Find the amount for each. (3 marks) 13. Draw a flowchart showing the steps to find the selling price when cost price and profit percent are given, and apply it to CP = Rs 800 and profit = 15%. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Juhi sells a washing machine for Rs 13,500 and loses 20%. (i) Find the cost price. (ii) At what price should she have sold it to gain 10%? (iii) Explain why the loss is not 20% of the selling price. (iv) Find the loss amount. (5 marks) 15. Mohan borrows Rs 56,000 at 12% per year simple interest. (i) Find the interest for 2 years. (ii) Find the amount to be repaid. (iii) In how many years will the interest become Rs 33,600? (iv) Would borrowing for longer increase the interest? Explain. (5 marks) 16. A student scored 320 out of 400 in Term 1 and 405 out of 500 in Term 2. (i) Find the percentage in each term. (ii) In which term did the student do better? (iii) Why is it better to compare percentages rather than marks? (iv) What is the percentage increase in marks from 320 to 405? Round to one decimal place. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Write the formula before every calculation and show all steps.