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Ratio, Proportion & Percentages

Ratio, Proportion & Percentages — Free MYP3 Mathematics Practice Questions

1QuestionSolving Problems Involving Direct ProportionConcept Practice

3 marks~5 minCriterion C

A supermarket sells flour in bulk. 5 kg of flour costs 12.50 dollars.

Calculate the cost of 1 kg of flour using the unitary method. [1]

Calculate the cost of 8 kg of flour. Show your working. [1]

A customer says: "10 kg of flour would cost exactly double the price of 5 kg, so buying 10 kg is no better value than buying 5 kg." Explain whether the customer is correct, and what this tells you about the relationship between mass and cost. [1]

Solutions

2QuestionUnderstanding Direct Proportion RelationshipsConcept Practice

3 marks~5 minCriterion A

A market stall sells rice in different bag sizes. A 2 kg bag costs 4 dollars. The price is directly proportional to the weight.

Calculate the cost of a 5 kg bag. [1]

Explain what it means for price to be directly proportional to weight in this context. [1]

A 10 kg bag is advertised at 15 dollars. Explain whether this price is consistent with the direct proportion model, and suggest one reason why the price may differ. [1]

Solutions

3QuestionSolving Percentage Increase and Decrease ProblemsConcept Practice

3 marks~5 minCriterion A

A clothing store buys a shirt for 12 dollars. The store applies a markup of 40% to set the selling price.

Calculate the selling price of the shirt. [1]

The actual cost price may vary by up to 5% due to supplier changes. Explain how a 5% increase in cost price would affect the store's profit. [1]

The store is considering two pricing strategies: a fixed 40% markup, or adjusting the markup based on competitor prices. Analyse one advantage and one disadvantage of using a fixed markup. [1]

Solutions

4QuestionCalculating Percentage ChangeConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of 8 cm and a width of 5 cm. The length is increased by 25%.

(a) Calculate the new length of the rectangle. Show your working. [2]

Solutions

5QuestionReal-World Applications of Reverse PercentageConcept Practice

2 marks~3 minCriterion A

A jacket has an original price of

25 \text{ USD}

. A shop sells it for

80\%

of the original price.

Calculate the sale price of the jacket. [2]

Solutions

6QuestionSolving Net Price and Final Cost ProblemsConcept Practice

3 marks~5 minCriterion A

The graph below shows the relationship between discount percentage and net price for an item with an original price of 80 dollars.

Discount (%)	0	10	20	30	40	50
Net price (dollars)	80	72	64	56	48	40

Describe the relationship between discount percentage and net price shown in the graph. [1]

Calculate the net price when the discount is 35%. [1]

A 10% tax is applied to the net price after the 35% discount. Calculate the final cost of the item. [1]

Solutions

7QuestionDefining Ratios and Their NotationConcept Practice

2 marks~3 minCriterion A

A rectangle is divided into 7 equal sections. Four sections are shaded and three sections are unshaded.

Calculate the ratio of shaded sections to unshaded sections. Express your answer in the form

a:b

. [2]

Solutions

8QuestionAdjusting Quantities Using RatiosConcept Practice

2 marks~3 minCriterion B

A pancake recipe uses the following amounts:

Number of pancakes	2	4	6	8
Eggs	1	2	3	4
Flour (g)	100	200	300	400

Describe the relationship between the number of pancakes and the amount of each ingredient. [1]

State the rule you would use to calculate the number of eggs and the amount of flour needed for any number of pancakes. [1]

Solutions

9QuestionAdjusting Quantities Using RatiosConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths in the ratio

3:2

. The longer side measures

6

cm.

(a) Calculate the length of the shorter side. [2]

Solutions

10QuestionSolving Problems Involving Direct ProportionAssessment Practice

6 marks~9 minCriterion D

A construction company lays fibre-optic cable at a normal rate of 50 dollars per metre. For a 340 m stretch, 120 m passes through rocky ground where the cost per metre is 15% higher than the normal rate.

Calculate the total cost for the 340 m stretch. [2]

Explain why using a single constant rate of 50 dollars per metre for the entire 340 m would not give an accurate cost estimate. [2]

The company budgets using the constant rate of 50 dollars per metre for the full 340 m. Analyse how this affects the project, and justify whether the company should revise its budgeting method. [2]

Solutions

11QuestionSolving Problems Involving Direct ProportionAssessment Practice

6 marks~9 minCriterion B

The table below shows three squares and their diagonal lengths, calculated using the Pythagorean theorem.

Side length (cm)	2	3	5
Diagonal length (cm)	2.83	4.24	7.07

Calculate the ratio of diagonal to side length for each square in the table. What do you notice? [2]

Explain how the constant ratio from part (a) can be used to find the diagonal of a square with side length 7 cm. Show your working. [2]

A student claims: "The longer the side of a square, the greater the ratio of diagonal to side length." Analyse this claim using the general relationship between side length

s

and diagonal

d

. [2]

Solutions

12QuestionApplications of Compound Interest and DepreciationAssessment Practice

8 marks~12 minCriterion D

A student borrows 2000 dollars to buy a phone. The bank charges compound interest at 8% per year. After 2 years, the bank offers a 5% discount on the total amount owed if the student repays in full at that point.

Calculate the total amount owed after 2 years. [2]

Calculate the amount the student pays after the discount is applied. [2]

Analyse one reason why this compound interest model may not fully represent the real cost of the loan. Use your answer to explain whether the student should repay early. [4]

Solutions

13QuestionFinding a Percentage of a QuantityAssessment Practice

7 marks~11 minCriterion C

A clothing store advertises a jacket priced at 120 dollars with a sale offering "30% off, then an extra 20% off the reduced price."

Calculate the final price after both discounts are applied in sequence. [2]

The store claims the total saving is "50% off" because

30\% + 20\% = 50\%

. Calculate the actual total discount percentage and explain why the store's claim is incorrect. [3]

A rival store offers a single discount of 44% off the same jacket. Compare the two discount methods and justify which offer gives the better deal for the customer. [2]

Solutions

14QuestionSolving Percentage Increase and Decrease ProblemsAssessment Practice

7 marks~11 minCriterion B

A store sells an item priced at 250 dollars. Store A applies a 20\% discount first, then adds 10\% sales tax. Store B adds the 10\% sales tax first, then applies the 20\% discount.

Calculate the final price at each store. [2]

Explain why both stores produce the same final price. [2]

A classmate says: "The order will always give the same price, no matter what." Analyse this claim by identifying one situation where the final prices could differ in practice. [3]

Solutions

15QuestionCalculating Percentage ChangeAssessment Practice

2 marks~3 minCriterion D

A student's monthly allowance increases from 40 dollars to 46 dollars.

Calculate the percentage increase in the allowance. Show your working. [1]

Explain one limitation of using percentage change when comparing allowances of different sizes. [1]

Solutions

16QuestionSolving Real-Life Percent Change ScenariosAssessment Practice

4 marks~6 minCriterion C

A video game costs 45 dollars. A store applies a 20% discount and an 8% sales tax.

Calculate the final price when the discount is applied before the tax. [1]

Explain why applying the tax before the discount gives the same final price. Name the mathematical property that justifies this. [2]

Describe one real-world situation where the order of applying a discount and a tax would produce a different final price. [1]

Solutions

17QuestionComparing Percentage Gains and LossesAssessment Practice

3 marks~5 minCriterion B

A student invests 100 dollars in each of two stocks for two months.

Stock A gains 25% in month one, then loses 20% in month two.
Stock B loses 20% in month one, then gains 25% in month two.

The student claims both stocks finish at the same value because they experience the same percentage changes.

Calculate the final value of each stock. [1]

Explain whether the student's claim is correct. [1]

A different investor applies a 50% gain followed by a 50% loss to a 100 dollar investment. Analyse what this result shows about assuming that equal percentage gains and losses always cancel out. [1]

Solutions

18QuestionReal-World Applications of Reverse PercentageAssessment Practice

5 marks~8 minCriterion B

Three stores are selling discounted items. The sale price and percentage decrease are known for each store.

Store A: A jacket costs 72 dollars after a 10% decrease.
Store B: A laptop costs 136 dollars after a 15% decrease.
Store C: A television costs 255 dollars after a 25% decrease.

Calculate the original price of the jacket in Store A. [1]

Calculate the original price of the laptop in Store B. [1]

A fourth store sells a games console for

F

dollars after a percentage decrease of

r

(as a decimal). Using the pattern from parts (a) and (b), write a formula for the original price

O

in terms of

F

and

r

. Justify your formula by showing how it applies to Store C. [3]

Solutions

19QuestionFinding Original Amounts Before ChangeAssessment Practice

6 marks~9 minCriterion C

A clothing shop marks up items by 30% above cost price. During a sale, it then applies a 25% discount to the marked price. A customer claims the final sale price is 5% above the original cost price.

The final sale price of a jacket is 78 dollars. Calculate the original cost price. [2]

Explain why the customer's claim is incorrect, showing the actual percentage difference between the final sale price and the original cost price. [2]

Justify why adding and subtracting percentages directly (30% − 25% = 5%) gives the wrong result in this situation. [2]

Solutions

20QuestionFinding Original Amounts Before ChangeAssessment Practice

4 marks~6 minCriterion D

A store sells a phone for 340 dollars after applying a 15% discount. The store's pricing model assumes a fixed 15% discount on all phones, regardless of stock levels, seasonal demand, or competitor pricing.

Calculate the original price of the phone before the discount. Show your working clearly. [2]

Explain why a fixed 15% discount may not reflect real-world retail pricing. [2]

Solutions

21QuestionApplying Multiple Percent Changes TogetherAssessment Practice

2 marks~3 minCriterion C

A store applies a 15\% discount to an item and then adds 9\% sales tax on the discounted price. The owner claims the final price is 94\% of the original price.

State one assumption the owner makes about how the two percent changes are combined. [1]

Calculate the actual final price as a percentage of the original price. Show your working clearly. [1]

Solutions

22QuestionApplying Multiple Percent Changes TogetherAssessment Practice

8 marks~12 minCriterion B

A jacket has an original price of 200 dollars. A store applies three changes in this order: a 20% discount, then 8% GST, then an additional 10% discount.

Calculate the final price the customer pays after all three changes are applied. Show all working. [3]

A second store applies the same three percentages in a different order: 8% GST first, then 20% discount, then 10% discount. Calculate the final price and explain whether it differs from part (a). [3]

The table below shows how two stores advertise the same jacket.

Store A: "20% off, then 10% off!"
Store B: "Save 30%!"

Analyse which store offers the better deal for the customer. Support your answer with calculations. [2]

Solutions

23QuestionApplying Multiple Percent Changes TogetherAssessment Practice

4 marks~6 minCriterion D

A small business owner makes handmade wooden coasters. Each coaster costs 5 dollars in materials. The selling price is 20 dollars. During a sale, a

15\%

discount is applied, followed by

10\%

tax on the discounted price.

Calculate the final price a customer pays for one coaster. [2]

Explain whether the model

\text{Final price} = 20 \times 0.85 \times 1.10

accurately represents the owner's profit per coaster. [2]

Solutions

24QuestionDefining Ratios and Their NotationAssessment Practice

6 marks~9 minCriterion C

A student claims: "If two ratios are equivalent, their cross-products are equal. So

3:5

and

9:15

are equivalent."

Calculate the cross-products of

3:5

and

9:15

, and state whether the ratios are equivalent. [2]

Explain why the ratio

2.5:3.75

is equivalent to

2:3

, using cross-products to support your answer. [2]

A second student claims: "The only ratio equivalent to

2:3

4:6

." Analyse this claim and justify whether it is true or false. [2]

Solutions

25QuestionDefining Ratios and Their NotationAssessment Practice

8 marks~12 minCriterion D

A cartographer draws a map using a scale of 1:50,000, meaning 1 cm on the map represents 50,000 cm in reality. After printing, humidity causes the paper to shrink by 2%. A distance measured on the shrunken map is 12 cm.

Calculate the actual distance represented by 12 cm on the map, assuming no shrinkage has occurred. [2]

Explain how a 2% shrinkage systematically affects all distances on the map, and calculate the new scale after shrinkage. [3]

Analyse two real-world factors that limit the reliability of a fixed map scale, and identify one method that reduces the impact of these factors. [3]

Solutions

26QuestionDefining Ratios and Their NotationAssessment Practice

7 marks~11 minCriterion B

A 4 × 4 grid has 16 squares: 6 red and 10 blue, giving a red : blue ratio of

6:10 = 3:5

A 4 × 4 grid uses 16 squares, which is a multiple of 8 (since

3 + 5 = 8

). Calculate the smallest square grid whose total number of squares is also a multiple of 8, and state how many red and blue squares it would contain at ratio

3:5

. [2]

A 10 × 10 grid has 100 squares. Calculate the number of red squares and the number of blue squares needed to keep the ratio

3:5

exactly. [2]

A student claims: "Any square grid can keep the red : blue ratio exactly equal to

3:5

." Using your results from parts (a) and (b), explain whether this claim is correct. [3]

Solutions

27QuestionAdjusting Quantities Using RatiosAssessment Practice

3 marks~5 minCriterion C

A cookie recipe for 12 servings uses 240 g of flour and 180 g of butter.

Calculate the scale factor needed to adjust the recipe from 12 servings to 30 servings. [1]

Calculate the amount of flour needed for 30 servings. [1]

A friend says: "I only need 18 servings, so I should use more flour than the original recipe." Explain whether your friend is correct, supporting your answer with a calculation. [1]

Solutions

28QuestionAdjusting Quantities Using RatiosAssessment Practice

8 marks~12 minCriterion D

A chef is preparing a pasta sauce for a charity dinner. The recipe serves 8 people and uses tomatoes, onions, and garlic in the ratio

3:2:1

by mass, with a total mass of

6

kg. The chef needs to serve 50 people. Ingredients can only be purchased in increments of

0.5

kg.

Calculate the mass (in kg) of each ingredient needed to serve 50 people. [2]

The chef rounds each quantity from part (a) to the nearest

0.5

kg. Calculate the rounded mass of each ingredient and explain why this rounding may cause a problem when preparing the sauce. [3]

Analyse how rounding the ingredient quantities affects the ratio of tomatoes to garlic, and discuss one limitation of using a simple ratio to scale a recipe to a much larger quantity. [3]

Solutions