Mathematics • Year 8 • Unit 1 • Lesson 10

Percentage Profit and Loss

Build fluency with percentage profit and loss — ALWAYS taken on the cost price (CP), never the selling price. Use the formula profit/CP × 100, and reverse to find SP from a target % profit.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. This is the classic "mango profit" — turn a $1 markup into a percentage profit on cost.

Problem. A stall buys mangoes for $2 each (CP) and sells them for $3 each (SP). Find the percentage profit.

Step 1 — Find the profit in dollars per mango.

Profit = SP − CP = 3 − 2 = $1

Reason: SP minus CP gives the dollar profit per item.

Step 2 — Set up the percentage formula.

% profit = (profit ÷ CP) × 100 = (1 ÷ 2) × 100

Reason: ALWAYS divide by CP, never SP. CP is the "base" — what was risked.

Step 3 — Compute.

(1 ÷ 2) × 100 = 0.5 × 100 = 50%

Reason: convert the decimal fraction to a percentage by × 100.

Step 4 — Sanity check by reversing.

SP = CP × (1 + 0.50) = 2 × 1.50 = $3 ✓

Reason: 50% profit on $2 means × 1.50, which gives $3 — matches the original SP.

Answer: 50% profit on cost (also called a 50% markup).

Stuck? Revisit lesson § Card 5 — "% profit = profit/CP × 100. CP is the base, not SP. A common Year 8 trap is dividing by $3 instead of $2."

2. We do — fill in the missing steps

Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks

Problem. A laptop bought for $1200 is sold for $960. Find the percentage loss.

Step 1 — Find the loss in dollars:

Loss = CP − SP = ______ − ______ = $______

Step 2 — Set up the formula (use CP as base):

% loss = (loss ÷ CP) × 100 = (______ ÷ ______) × 100

Step 3 — Compute:

______ × 100 = ______%

Step 4 — Final answer:

______% ______ (profit or loss)

Stuck? CP is $1200 (the original price). Loss/CP = 240/1200 = 0.20.

3. You do — independent practice

Show your working under each problem. The first four are foundation (clean % from given CP and SP). The middle two are standard (compute % loss). The last two are extension (find SP from CP and target %).

Foundation — given CP and SP, find % profit

3.1 CP $40, SP $50. Find the % profit. 1 mark

3.2 CP $25, profit $10. Find the % profit. 1 mark

3.3 A book bought for $20 sold for $25. % profit? 1 mark

3.4 CP $80, SP $100. % profit? 1 mark

Standard — compute % loss

3.5 CP $200, SP $160. Find the % loss. 2 marks

3.6 CP $240, SP $192. Find the % loss. 2 marks

Extension — find SP from CP and a target %

3.7 CP $80 at 50% profit. What is the SP? 2 marks

3.8 A trader buys an item for $400 and wants a 35% profit. What should they sell it for? 2 marks

Stuck on 3.7 / 3.8? SP = CP × (1 + P/100). 50% profit ⇒ × 1.50; 35% profit ⇒ × 1.35.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do ($1200 → $960 laptop)

Step 1: Loss = 1200 − 960 = $240.
Step 2: % loss = (240 ÷ 1200) × 100.
Step 3: 0.20 × 100 = 20%.
Step 4: 20% loss.

3.1 — CP $40, SP $50

Profit = $10. % profit = (10/40) × 100 = 25% profit.

3.2 — CP $25, profit $10

% profit = (10/25) × 100 = 40% profit.

3.3 — Book $20 → $25

Profit = $5. % profit = (5/20) × 100 = 25% profit.

3.4 — CP $80, SP $100

Profit = $20. % profit = (20/80) × 100 = 25% profit.

3.5 — CP $200, SP $160

Loss = $40. % loss = (40/200) × 100 = 20% loss.

3.6 — CP $240, SP $192

Loss = $48. % loss = (48/240) × 100 = 20% loss.

3.7 — CP $80 at 50% profit

SP = 80 × 1.50 = $120. (Check: profit $40; % profit = 40/80 × 100 = 50% ✓.)

3.8 — CP $400 at 35% profit

SP = 400 × 1.35 = $540. (Check: profit $140; % profit = 140/400 × 100 = 35% ✓.)