A medium question on percentages and mixtures for P5–P6, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P6 first round and finals: discounts, a rise followed by a fall, and mixtures.
The question
The lunch set at a cha chaan teng costs $50.
When costs go up, the price is raised by 20%.
A month later, to win back customers, the price at that time is cut by 20%.
What does the lunch set cost now?
Show the hints (2)
💡Hint 1: The second change of 20% — a percentage of which price?
💡Hint 2: First find the price after the rise, then treat that as the new 100%.
Worked solution
Have a go first, then read the solution step by step.
1.The rise is a percentage of the original $50: $50 × (100 + 20) ÷ 100 = $50 × 120 ÷ 100 = $60.
2.The cut is a percentage of $60: $60 × (100 − 20) ÷ 100 = $60 × 80 ÷ 100 = $48.
⚠️Common mistake: thinking a 20% rise and then a 20% cut gets back to $50. The second 20% is of $60, not $50, so the price ends $2 below where it started.
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