Question 1: A shop increases its prices by 20%. If a jacket originally costs £50, what is the new price after the increase? Show your working.

Answer: £60

Question 2: A car's value increases from £8,000 to £9,600 in one year. Calculate the percentage increase and identify the common mistake if someone calculates it as 20% without considering the actual change.

Answer: 20%; mistake: using original value instead of the change (£1,600) to find percentage increase

Question 3: A company's revenue increased from £150,000 to £180,000. What is the percentage increase? Show your working.

Answer: 20%

Question 4: A price increase was calculated as 25%, but the new price was actually £125 instead of the expected £130. Identify the mistake and explain it.

Answer: Incorrect percentage increase calculation; the actual increase was £25 on an original price of £100, which is 25%, but the new price should have been £125, so the calculation was correct, but perhaps original price was misunderstood.

Question 5: A student mistakenly thinks that increasing by 15% and then by another 15% gives a total increase of 30%. Explain why this is incorrect and calculate the actual total percentage increase.

Answer: Incorrect: successive percentage increases are multiplicative; actual increase = 1.15 × 1.15 = 1.3225, so total increase ≈ 32.25%

Question 6: A product's price increased by 10% in the first year and then decreased by 10% in the second year. What is the overall percentage change? Show your working.

Answer: Approximately 1% decrease

Question 7: In a sale, a jacket's price was reduced by 20%, and then later increased by 20%. What is the final price change relative to the original? Show your working.

Answer: Approximately 4% decrease

Question 8: A shopkeeper claims that increasing the price by 50% then decreasing it by 50% results in the original price. Is this true? Explain and justify your answer.

Answer: No, increasing by 50% and then decreasing by 50% does not return to the original price; it results in a 25% decrease overall.

Question 9: Identify the common error students make when calculating percentage increase based solely on the difference in price without dividing by the original amount.

Answer: Ignoring the division by the original value; mistake: using the difference (£20) as a percentage directly instead of dividing by the original (£100)

Question 10: A bicycle's price increased from £200 to £250. Calculate the percentage increase and explain why some students might miscalculate it as 25% without showing working.

Answer: 25%; common mistake: taking (250−200)/200=0.25 and converting to 25% without showing the calculation.

Question 11: A retailer claims a 40% profit margin on a product that costs £60 to produce. What should be the selling price? Show your working.

Answer: £84

Question 12: Challenge: A car's value decreases by 15% each year. Calculate its value after 3 years if the initial value is £20,000. Show your working.

Answer: Approximately £14,049