A hard question on percentages and mixtures for 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
A toy shop buys in a batch of model kits and marks them up 100% on cost.
In the anniversary sale they go at 20% off (80% of the marked price), and the shop still makes $126 on each one sold.
What does each model kit cost the shop?
Show the hints (3)
💡Hint 1: Call the cost 100 parts. How many parts is the marked price?
💡Hint 2: The sale price is 80% of the marked price — how many parts is that, and how many more than the cost?
💡Hint 3: The profit on each is 60 parts, and those 60 parts are $126.
Worked solution
Have a go first, then read the solution step by step.
1.Call the cost 100 parts: the marked price is 100 + 100 = 200 parts.
2.At 20% off: 200 × 80 ÷ 100 = 160 parts, which is 160 − 100 = 60 more than the cost.
3.60 parts are $126, so the cost, 100 parts, is 126 × 100 ÷ 60 = $210.
⚠️Common mistake: treating +100% then 20% off as a 100 − 20 = 80% profit. The discount is taken off the marked price, which is higher than the cost, so more than 20 parts come off.
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