Mathematics • Year 8 • Unit 1 • Lesson 10
Percentage Profit and Loss — Mixed Challenge
Pull together everything from Lesson 10: % profit, % loss, finding SP from a target %, and comparing margins. Six mixed problems, one "find the mistake" on dividing by SP instead of CP, and one open-ended pricing challenge.
1. Mixed problems — choose the right move
Each question uses a different combination of ideas from Lesson 10. Decide whether you are finding %, finding SP, or comparing margins before you start writing. Show your working. 3 marks each
1.1 CP $45, SP $72. Find the % profit.
1.2 CP $120 at 25% profit. Find the SP.
1.3 CP $80, SP $60. Find the % loss.
1.4 A trader makes 60% profit on cost. If CP is $50, find the SP.
1.5 Two market stalls sell apples. Stall A: CP $0.50, SP $0.80 per apple. Stall B: CP $0.40, SP $0.70 per apple. (a) Compute the % profit for each. (b) Which stall has the higher % profit?
1.6 CP $200 sold at a 15% loss. Find the SP and the dollar loss.
2. Find the mistake
A Year 8 student tried to find the % profit on a mango bought for $2 and sold for $3. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — CP $2, SP $3 mango, % profit:
Line 1: Profit = SP − CP = 3 − 2 = $1.
Line 2: The base for % profit is the SELLING price, because that's what we received.
Line 3: % profit = (profit ÷ SP) × 100 = (1 ÷ 3) × 100 ≈ 33.3%.
Line 4: Final answer: 33.3% profit.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected % profit.
Stuck? Revisit lesson § Card 5 — "% profit always uses COST PRICE as the base, not selling price."3. Open-ended challenge — pricing strategy
This question has more than one valid answer. 4 marks
3.1 You're starting a small T-shirt printing business. Each plain T-shirt costs you $8 (CP). You need to decide on your sale price (SP).
Design and justify a pricing strategy that meets BOTH of these goals:
(i) Each shirt must give you a percentage profit on cost between 40% and 80%.
(ii) The final SP must end in either $.00, $.50, or $.95 (typical retail pricing).
Your answer must include:
(a) Your chosen SP per shirt.
(b) The dollar profit per shirt.
(c) The exact % profit on cost (show working).
(d) A brief justification of why you chose that SP — what's the trade-off between charging more (higher margin) and charging less (more sales)?
Bonus: If you sell 200 T-shirts at your chosen SP, what is your total profit?
How did this worksheet feel?
What I'll revisit before next class:
1.1 — CP $45, SP $72
Profit = $27. % profit = (27/45) × 100 = 60% profit.
1.2 — CP $120 at 25% profit
SP = 120 × 1.25 = $150.
1.3 — CP $80, SP $60
Loss = $20. % loss = (20/80) × 100 = 25% loss.
1.4 — CP $50 at 60% profit
SP = 50 × 1.60 = $80.
1.5 — Two apple stalls
(a) Stall A: profit = $0.30; % profit = (0.30/0.50) × 100 = 60%. Stall B: profit = $0.30; % profit = (0.30/0.40) × 100 = 75%.
(b) Stall B has the higher % profit (75% vs 60%) even though both stalls make the same 30 cents per apple — Stall B's CP is lower, so the SAME 30c counts as a bigger fraction of their cost.
1.6 — CP $200 at 15% loss
SP = 200 × 0.85 = $170. Loss = 200 − 170 = $30 loss.
2 — Find the mistake
(a) The mistake is on Line 2 (the wrong base is then used in Line 3).
(b) % profit ALWAYS uses the COST PRICE as the base, not the selling price. CP is what was "risked" or "invested", so the profit is measured against that. Dividing by SP would give a margin-on-revenue measure (an advanced concept), but at Year 8 we always use CP.
(c) Corrected working:
Profit = 3 − 2 = $1.
% profit = (profit ÷ CP) × 100 = (1 ÷ 2) × 100 = 50% profit. ✓
Check: SP = CP × 1.50 = 2 × 1.50 = $3. ✓
3 — Open-ended challenge (sample strategy)
Sample strategy 1 — SP $12.00 (50% profit on cost):
(a) SP = $12.00. (b) Profit = 12 − 8 = $4 per shirt. (c) % profit = (4/8) × 100 = 50% — in the 40-80% range ✓. (d) Justification: $12 is a clean price that's neither too cheap nor too pricey for a typical T-shirt. A 50% margin gives a comfortable profit while keeping shirts attractive to students/parents.
Bonus: 200 × $4 = $800 total profit (if all 200 sell).
Sample strategy 2 — SP $13.95 (74.4% profit on cost):
(a) SP = $13.95. (b) Profit = 13.95 − 8 = $5.95 per shirt. (c) % profit = (5.95/8) × 100 = 74.4% — in range ✓. (d) Justification: the $.95 ending feels less than $14 to shoppers (psychological pricing). Higher margin per shirt, but may sell fewer.
Bonus: 200 × $5.95 = $1190 total profit (if all 200 sell).
Other valid SPs: $11.50 (43.75% profit), $12.50 (56.25%), $13.50 (68.75%), $14.00 (75%). Any SP between $11.20 and $14.40 ending in .00, .50, or .95 works.
Marking: 1 mark for a valid SP (40-80% range, ending in .00 / .50 / .95); 1 mark for correct dollar profit per shirt; 1 mark for correct % profit working; 1 mark for sensible justification AND correct bonus total. Multiple valid strategies — markers verify arithmetic only.