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 stationery shop buys in 30 school bags at $240 each, and marks them up 20% on cost.
Before term starts, some sell at the marked price; after term starts, the rest all sell at 25% off (75% of the marked price).
In the end the total profit is 14% of the total cost.
How many school bags sold at the marked price?
Show the hints (3)
💡Hint 1: First find what each school bag makes (or loses) at each price, then the total profit in dollars.
💡Hint 2: Suppose all 30 sold at the discount. What would the profit be, and how far is it from the real one?
💡Hint 3: Each one sold at the marked price instead adds $72; $1728 has to be made up.
Worked solution
Have a go first, then read the solution step by step.
4.If all 30 sold at the discount: a loss of 24 × 30 = $720, which is 1008 + 720 = $1728 away from the real $1008 profit.
5.Each one moved from the discount to the marked price adds 288 − 216 = $72: 1728 ÷ 72 = 24.
6.Check: 24 × 48 − 6 × 24 = $1008 ✓
⚠️Common mistake: assuming the discounted ones still make money. At 25% off each sells for $216, below the $240 cost — a loss that comes off the profit.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download