Unit 2 · Class 7 IB MYP · MCQ Test
Percentages & Proportional Reasoning MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Percentages & Proportional Reasoning — MCQ Questions
1A souvenir shop bought a sculpture for €120 and sold it for €150. What was the percentage profit for the shop?
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Answer: B. 25%
Hint: First, calculate the actual profit amount. Then, divide the profit by the original cost price and multiply by 100.
Solution:
Calculate the profit: Profit = Selling Price - Cost Price. — Profit = €150 - €120 = €30
Calculate the percentage profit: (Profit / Cost Price) × 100%. — Percentage Profit = (€30 / €120) × 100% = (1/4) × 100% = 25%
2A new smartphone is advertised for $960, which includes a 20% VAT (Value Added Tax). What was the original price of the smartphone before the VAT was added?
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Answer: B. $800
Hint: If the price includes 20% VAT, the advertised price represents 120% of the original price.
Solution:
Let the original price be 'P'. The price including VAT is P + 20% of P, which is 120% of P. — 120% of P = $960
Convert the percentage to a decimal: 1.20 × P = $960.
Solve for P by dividing the total price by 1.20. — P = $960 / 1.20 = $800
3If 7 identical books cost £56, how much would 12 of these books cost?
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Answer: B. £96
Hint: Find the cost of one book first. This is a common strategy in 'unitary method' problems.
Solution:
Find the cost of one book by dividing the total cost by the number of books. — Cost per book = £56 / 7 = £8
Multiply the cost of one book by the desired number of books. — Cost of 12 books = £8 × 12 = £96
4A car travels 210 km in 3 hours at a constant speed. How far will it travel in 5 hours at the same speed?
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Answer: C. 350 km
Hint: Since the speed is constant, distance and time are directly proportional. Find the speed (km per hour) first.
Solution:
Calculate the speed of the car (distance per unit of time). — Speed = 210 km / 3 hours = 70 km/hour
Multiply the speed by the new time to find the distance travelled. — Distance = 70 km/hour × 5 hours = 350 km
5After a 20% discount, a pair of running shoes costs €60. What was the original price of the running shoes before the discount?
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Answer: B. €75
Hint: If the shoes were discounted by 20%, the €60 price represents 80% of the original price.
Solution:
Let the original price be 'P'. After a 20% discount, the price is 100% - 20% = 80% of P. — 80% of P = €60
Convert the percentage to a decimal: 0.80 × P = €60.
Solve for P by dividing the discounted price by 0.80. — P = €60 / 0.80 = €75
6Alex wanted to find the new price of a book that originally cost $40 after a 15% increase. He calculated: $40 × 0.15 = $6, and then added this to the original price: $40 + $6 = $46. His friend Mia said he made a mistake. Which statement describes Alex's mistake, if any?
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Answer: D. Alex made no mistake; his calculation is correct.
Hint: Carefully review each step of Alex's calculation. Does it correctly represent a 15% increase?
Solution:
To find a 15% increase, you can either calculate 15% of the original amount and add it, or directly multiply the original amount by (1 + 0.15).
Alex calculated 15% of $40 (which is $6) and then added it to $40. This is a correct method to find a 15% increase. — $40 + (0.15 \times $40) = $40 + $6 = $46
Alternatively, $40 \times 1.15 = $46. Both methods yield the same correct result.
7Which statement correctly describes quantities that are directly proportional?
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Answer: B. If two quantities are directly proportional, their ratio is always constant.
Hint: Think about what happens to one quantity when the other is doubled or halved in a directly proportional relationship.
Solution:
Direct proportionality means that as one quantity increases, the other increases at a constant rate, and vice-versa. This implies a constant multiplier.
Mathematically, if y is directly proportional to x, then y = kx, where k is a constant. Rearranging this gives y/x = k. This means their ratio is constant.
8A baker uses 250g of flour and 150g of sugar for a cake. What percentage of the total dry ingredients (flour and sugar) is sugar?
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Answer: B. 37.5%
Hint: First, find the total mass of the dry ingredients. Then, express the mass of sugar as a percentage of this total.
Solution:
Calculate the total mass of dry ingredients. — Total dry ingredients = 250g (flour) + 150g (sugar) = 400g
Calculate the percentage of sugar relative to the total dry ingredients. — Percentage of sugar = (Mass of sugar / Total dry ingredients) × 100%
Substitute the values and calculate. — Percentage of sugar = (150g / 400g) × 100% = (3/8) × 100% = 37.5%
9A designer handbag initially costs €200. Its price increased by 10% for the new season, and then later decreased by 10% during a sale. What is the final price of the handbag?
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Answer: B. €198.00
Hint: Remember that a percentage change is always calculated based on the *current* amount, not the original amount, for each step.
Solution:
First, calculate the price after a 10% increase. — Price after increase = €200 × (1 + 0.10) = €200 × 1.10 = €220
Next, calculate the price after a 10% decrease on the *new* price. — Final Price = €220 × (1 - 0.10) = €220 × 0.90 = €198
10In a school library, the ratio of fiction books to non-fiction books is 5:3. If there are 240 books in total, what percentage of the books are fiction?
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Answer: C. 62.5%
Hint: First, determine the total number of parts in the ratio. Then, find the number of fiction books.
Solution:
Find the total number of parts in the ratio. — Total parts = 5 (fiction) + 3 (non-fiction) = 8 parts
Determine the number of books per part by dividing the total number of books by the total parts. — Books per part = 240 books / 8 parts = 30 books/part
Calculate the number of fiction books. — Number of fiction books = 5 parts × 30 books/part = 150 books
Calculate the percentage of fiction books. — Percentage fiction = (150 fiction books / 240 total books) × 100% = 0.625 × 100% = 62.5%
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Tips for Percentages & Proportional Reasoning MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Percentages & Proportional Reasoning MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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