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Lesson 10 ~25 min Unit 1 · Financial Maths +85 XP

Percentage Profit and Loss

Did the trader make a $50\%$ profit or just $20\%$? Compare deals fairly using percentages of cost price.

Today's hook: A market stall owner buys mangoes for $\$2$ each and sells them for $\$3$. What's the percentage profit?
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Think First
warm-up

A market stall owner buys mangoes for $\$2$ each and sells them for $\$3$. What's the percentage profit? Jot down your first reaction — then we'll see who's right.

Record your answer in your workbook.
1
The Big Idea
+5 XP

Percentage profit and loss are always taken on the COST PRICE — not the selling price. Formula: $\%$ profit $= \tfrac{\text{profit}}{\text{CP}} \times 100$.

You buy a mango for $\$2$ (CP) and sell it for $\$3$ (SP). Profit is $\$1$. As a percentage of the cost price: $\tfrac{1}{2} \times 100 = 50\%$ profit. Always divide by CP, not SP. A $50\%$ profit doesn't mean half the SP; it means half OF the cost was the profit.

$\%$ Profit $= \dfrac{\text{Profit}}{\text{CP}} \times 100$
Always on CP
$\%$ profit/loss uses the COST price as the base.
Profit on top
$\tfrac{\text{profit}}{\text{CP}}$, then times 100.
Loss is the same idea
$\%$ loss $= \tfrac{\text{loss}}{\text{CP}} \times 100$.
2
What You'll Master
objectives

Know

  • $\%$ profit $= \tfrac{\text{profit}}{\text{CP}} \times 100$
  • $\%$ loss $= \tfrac{\text{loss}}{\text{CP}} \times 100$
  • CP is always the base, never SP
  • Profit can be over $100\%$ of CP if SP is more than double

Understand

  • Why CP is the base — it's what was risked
  • How $\%$ profit gives a fair comparison across deals
  • That $\%$ loss has the same structure

Can Do

  • Compute $\%$ profit or loss given CP and SP
  • Solve for SP given CP and $\%$ profit
  • Compare two deals using percentages instead of absolute dollars
3
Words You Need
vocabulary
Percentage profitProfit expressed as a fraction of cost price, $\times 100$.
Percentage lossLoss expressed as a fraction of cost price, $\times 100$.
MarkupThe added amount above CP — same as profit on cost.
MarginSometimes used for profit as $\%$ of SP (advanced).
Cost-baseThe CP — used as denominator in profit %.
Return on costSame as percentage profit.
4
Spot the Trap
heads-up

Wrong: "$\$1$ profit on $\$3$ sale = $\tfrac{1}{3} \times 100 = 33\%$ profit" — NO. The base is CP ($\$2$), not SP. Real profit is $50\%$.

Right: Base is CP: $\tfrac{1}{2} \times 100 = 50\%$.

Wrong: "$\%$ loss = loss as $\%$ of SP" — NO. Loss is always as a $\%$ of CP.

Right: Loss is $\%$ of CP: $\tfrac{\text{loss}}{\text{CP}} \times 100$.

5
Percentage Profit
+5 XP

Profit divided by cost price, times 100.

A book bought for $\$15$ (CP) sells for $\$24$ (SP). Profit $= 24 - 15 = \$9$. $\%$ profit $= \tfrac{9}{15} \times 100 = 60\%$. So the seller earns $60\%$ on top of cost. This is sometimes called a $60\%$ markup.

$\%$ Profit $= \dfrac{\text{Profit}}{\text{CP}} \times 100$
Profit/CP
Top is profit, bottom is cost.
Times 100
To convert decimal to percentage.
Markup = $\%$ profit
Same formula, different name.
6
Percentage Loss
+5 XP

Same structure as profit — just using the loss amount.

A car bought for $\$8000$ is sold for $\$5600$. Loss $= 8000 - 5600 = \$2400$. $\%$ loss $= \tfrac{2400}{8000} \times 100 = 30\%$. The seller lost $30\%$ of what they originally paid.

$\%$ Loss $= \dfrac{\text{Loss}}{\text{CP}} \times 100$
Same structure
Loss replaces profit in the top.
Base is still CP
Never use SP as the base.
Always positive value
Loss is reported as a positive percentage.

Watch Me Solve It · 3 examples

Watch Me Solve It · The mango
+15 XP per step
Q1
PROBLEM
A stall buys mangoes for $\$2$ each and sells for $\$3$. Find the percentage profit.
  1. 1
    Profit per mango
    $3 - 2 = \$1$
    SP minus CP.
  2. 2
    Profit/CP
    $\tfrac{1}{2}$
    Always on the cost.
  3. 3
    $\times 100$
    $\tfrac{1}{2} \times 100 = 50\%$
    That's the percentage profit.
Answer$50\%$ profit
Watch Me Solve It · % loss
+15 XP per step
Q2
PROBLEM
A laptop bought for $\$1200$ is sold for $\$960$. Find the percentage loss.
  1. 1
    Loss
    $1200 - 960 = \$240$
    CP minus SP.
  2. 2
    Loss/CP
    $\tfrac{240}{1200}$
    Loss as fraction of cost.
  3. 3
    $\times 100$
    $0.20 \times 100 = 20\%$
    $20\%$ loss.
Answer$20\%$ loss
Watch Me Solve It · Find SP from % profit
+15 XP per step
Q3
PROBLEM
A trader buys an item for $\$400$ and wants a $35\%$ profit. What should they sell it for?
  1. 1
    Multiplier method
    SP $= $ CP $\times (1 + 0.35) = $ CP $\times 1.35$
    $35\%$ markup means $\times 1.35$.
  2. 2
    Compute
    $400 \times 1.35 = \$540$
    Selling price.
  3. 3
    Check
    Profit $= 540 - 400 = \$140$; $\tfrac{140}{400} \times 100 = 35\%$ ✓
    Confirmed.
Answer$\$540$

Common Pitfalls

8
Common Pitfalls
heads-up
Using SP as the base
Dividing profit by SP gives the wrong $\%$.
Fix: $\%$ profit divides by CP, always.
Confusing markup with margin
“Margin” often means profit as $\%$ of SP (different formula).
Fix: At Year 8, use markup = profit/CP × 100.
Forgetting to multiply by 100
$\tfrac{9}{15} = 0.6$ — that's not $60\%$ yet.
Fix: Always finish with $\times 100$.
Copy Into Your Books

$\%$ Profit

  • $\tfrac{\text{profit}}{\text{CP}} \times 100$
  • Base = CP
  • Markup = $\%$ profit

$\%$ Loss

  • $\tfrac{\text{loss}}{\text{CP}} \times 100$
  • Base = CP
  • Positive amount

Find SP from $\%$

  • SP = CP $\times (1 + \tfrac{P}{100})$
  • Loss: SP = CP $\times (1 - \tfrac{P}{100})$
  • One-step multiplier

Quick examples

  • CP $\$50$, $25\%$ profit $\to$ SP $\$62.50$
  • CP $\$60$, $10\%$ loss $\to$ SP $\$54$
  • SP $\$120$, CP $\$80 \to 50\%$ profit

How are you completing this lesson?

Brain Trainer · 4 problems

D
Brain Trainer · Percentage Profit and Loss
4 problems

Four drill problems to sharpen your skills. Work each, then reveal the answer.

  1. 1 CP $\$40$, SP $\$50$. $\%$ profit?

    $\tfrac{10}{40} \times 100 = 25\%$.$25\%$

  2. 2 CP $\$200$, SP $\$160$. $\%$ loss?

    $\tfrac{40}{200} \times 100 = 20\%$.$20\%$

  3. 3 CP $\$80$ at $50\%$ profit. SP?

    $80 \times 1.50 = \$120$.$\$120$

  4. 4 CP $\$25$, profit $\$10$. $\%$ profit?

    $\tfrac{10}{25} \times 100 = 40\%$.$40\%$
Complete in your workbook.

Quick Check · 5 questions

1
A book bought for $\$20$ is sold for $\$25$. The percentage profit is:
+10 XP
2
A car bought for $\$15\,000$ sold for $\$12\,000$. % loss:
+10 XP
3
CP is $\$120$. A $25\%$ profit means selling for:
+10 XP
4
CP $\$80$, SP $\$60$. Outcome:
+10 XP
5
A trader makes $60\%$ profit on cost. If CP is $\$50$, SP is:
+10 XP

Show Your Working · 3 questions

Show Your Working
9 marks total
Apply Medium 3 MARKS

Q6. Compute % profit or loss: (a) CP $\$80$, SP $\$100$; (b) CP $\$240$, SP $\$192$; (c) CP $\$45$, SP $\$72$.

Answer in your workbook.
Understand Easy 2 MARKS

Q7. A bakery wants $30\%$ profit on its $\$8$ CP cakes. (a) What SP should they set? (b) What is the profit per cake?

Answer in your workbook.
Reason Hard 4 MARKS

Q8. Two clothing brands sell similar shirts. Brand A makes $\$15$ profit on each shirt with CP $\$30$. Brand B makes $\$20$ profit on each shirt with CP $\$80$. (a) Calculate % profit for each. (b) Which has the higher percentage profit per shirt? (c) Explain why a higher dollar profit doesn't always mean a better margin.

Answer in your workbook.
Comprehensive Answers

Quick Check

1. C — $25\%$ profit.

2. A — $20\%$ loss.

3. D — $\$150$.

4. B — $25\%$ loss.

5. C — $\$80$.

Show Your Working Model Answers

Q6 (3 marks): (a) Profit $\$20$; $\tfrac{20}{80} \times 100 = 25\%$ profit [1]. (b) Loss $\$48$; $\tfrac{48}{240} \times 100 = 20\%$ loss [1]. (c) Profit $\$27$; $\tfrac{27}{45} \times 100 = 60\%$ profit [1].

Q7 (2 marks): (a) SP $= 8 \times 1.30 = \$10.40$ [1]. (b) Profit $= \$2.40$ per cake [1].

Q8 (4 marks): (a) A: $\tfrac{15}{30} \times 100 = 50\%$. B: $\tfrac{20}{80} \times 100 = 25\%$ [2]. (b) Brand A has the higher % profit ($50\%$ vs $25\%$) [1]. (c) Brand B makes more dollars per shirt ($\$20$ vs $\$15$), but as a fraction of cost, brand A is much more efficient — twice the markup on each dollar invested [1].

Stretch Challenge · +25 XP, +10 coins

The Restoration Project

You buy a broken bicycle for $\$80$. You spend $\$45$ on parts and clean it up. You sell the restored bike for $\$220$. (a) What is your TOTAL CP? (b) What is your profit in dollars? (c) What is your percentage profit on total cost?

Reveal solution

(a) Total CP $= 80 + 45 = \$125$. (b) Profit $= 220 - 125 = \$95$. (c) $\%$ profit $= \tfrac{95}{125} \times 100 = 76\%$. A very healthy markup — but only because labour wasn't counted in CP. Including time, the real ROI is lower.

R
Quick Review

Always on CP

Base for % profit/loss

Profit/CP

Times 100

Loss/CP

Times 100

Markup

Same as % profit

SP from %

CP × (1 + r) for profit

Fair comparison

% beats raw dollars

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