About Percentages & Proportional Reasoning — Class 7 IB

Calculate percentages, discounts, and markups; solve proportional reasoning problems. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 2). On this page you can practice 50 questions across three difficulty levels — 10 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Percentages & Proportional Reasoning

• Introduction to Percentages
• Calculating Percentages of Quantities
• Percentage Increase and Decrease
• Proportional Reasoning: Unitary Method
• Direct Proportion

Interactive lesson · about 75 minutes · checkpoint question after every unit

Percentages & Proportional Reasoning — solved examples for Class 7 IB

Practice questions on Percentages & Proportional Reasoning

1. Q1.easy

   A 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?

   1. A)A. $768
   2. B)B. $800
   3. C)C. $720
   4. D)D. $900
   Show answer

   Answer: B. $800

   Hint: If the price includes 20% VAT, the advertised price represents 120% of the original price.

2. Q2.easy

   If 7 identical books cost £56, how much would 12 of these books cost?

   1. A)A. £84
   2. B)B. £96
   3. C)C. £108
   4. D)D. £112
   Show answer

   Answer: B. £96

   Hint: Find the cost of one book first. This is a common strategy in 'unitary method' problems.

3. Q3.easy

   A car travels 210 km in 3 hours at a constant speed. How far will it travel in 5 hours at the same speed?

   1. A)A. 300 km
   2. B)B. 320 km
   3. C)C. 350 km
   4. D)D. 380 km
   Show answer

   Answer: C. 350 km

   Hint: Since the speed is constant, distance and time are directly proportional. Find the speed (km per hour) first.

4. Q4.medium

   A new drone was priced at €350. During a holiday sale, its price dropped to €297.50. What was the percentage decrease in the drone's price?

   1. A)10%
   2. B)15%
   3. C)20%
   4. D)25%
   Show answer

   Answer: 15%

   Hint: Find the amount of the price drop first, then calculate what percentage that drop is of the original price.

5. Q5.medium

   A jacket in a London boutique has an original price of £80. If there's a 25% discount, how much will a customer pay for the jacket?

   1. A)£60
   2. B)£65
   3. C)£70
   4. D)£75
   Show answer

   Answer: £60

   Hint: You can either calculate the discount amount and subtract it, or directly calculate the percentage of the original price that remains after the discount.

6. Q6.medium

   A small café buys coffee beans for $15 per kilogram. To cover costs and make a profit, they mark up the price by 60%. What is the selling price per kilogram of coffee beans?

   1. A)$21
   2. B)$22.50
   3. C)$23
   4. D)$24
   Show answer

   Answer: $24

   Hint: Calculate the amount of the markup, then add it to the original cost price to find the selling price.

7. Q7.hard

   A rare species of bird saw its population decrease by 20% due to habitat loss. The current population is 1600 birds. Alex calculated the original population by adding 20% to 1600, reaching 1920 birds. What was Alex's mistake?

   1. A)He should have subtracted 20% from 1600.
   2. B)He incorrectly assumed the 20% decrease was based on the current population.
   3. C)The 20% decrease should have been calculated from the original population, not the current population.
   4. D)He calculated the percentage change incorrectly, it should be a fraction.
   Show answer

   Answer: The 20% decrease should have been calculated from the original population, not the current population.

   Hint: The percentage decrease always refers to a percentage of the *original* amount. Consider what percentage of the original population 1600 represents.

8. Q8.hard

   A designer backpack originally priced at €250 in Paris is on sale with a 20% discount. After the discount, a Value Added Tax (VAT) of 15% is applied to the discounted price. What is the final price of the backpack?

   1. A)€210.00
   2. B)€220.00
   3. C)€230.00
   4. D)€237.50
   Show answer

   Answer: €230.00

   Hint: Remember to apply the discount first, and then calculate the VAT on the new, discounted price. Order of operations matters in multi-step percentage problems.

9. Q9.hard

   During a flash sale, a smart tablet was sold for $340 after a 15% discount. What was the original price of the tablet before the discount?

   1. A)$380
   2. B)$390
   3. C)$400
   4. D)$410
   Show answer

   Answer: $400

   Hint: If an item is sold at a 15% discount, the selling price represents 100% - 15% of the original price. Use this to work backwards.

These are 9 of the 50 questions available for Percentages & Proportional Reasoning. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.