Lesson 9 ~25 min Unit 1 · Financial Maths +85 XP

Profit and Loss

When you buy and sell, did you make money or lose it? Cost price, selling price, profit, loss.

Today's hook: You buy a second-hand phone for $\$200$ and sell it for $\$175$. Did you make a profit or loss? How much?

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Think First

warm-up

You buy a second-hand phone for $\$200$ and sell it for $\$175$. Did you make a profit or loss? How much? Jot down your first reaction — then we'll see who's right.

Record your answer in your workbook.

The Big Idea

+5 XP

Profit happens when SP $>$ CP. Loss happens when SP $<$ CP. The amount is just SP $-$ CP (or CP $-$ SP, depending on which is bigger). Easy maths — but watch the wording.

You buy at the cost price (CP) and sell at the selling price (SP). If SP $>$ CP, the difference is your profit. If SP $<$ CP, the difference is your loss. A phone bought for $\$200$ and sold for $\$175$: $200 - 175 = \$25$ loss.

Profit $= $ SP $- $ CP Loss $= $ CP $-$ SP

Buy = CP

Cost price is what YOU paid.

Sell = SP

Selling price is what someone paid YOU.

Direction matters

Profit needs SP > CP. Otherwise, loss.

What You'll Master

objectives

Know

Cost price (CP): what you paid
Selling price (SP): what you receive
Profit = SP − CP when SP > CP
Loss = CP − SP when SP < CP
Profit and loss are always positive amounts

Understand

Why profit cannot be negative (loss is the opposite)
How marked price differs from selling price (marked > selling sometimes)
The role of CP in determining percentage profit/loss

Can Do

Compute profit or loss given CP and SP
Identify whether a transaction made money
Solve word problems involving buying and selling

Words You Need

vocabulary

Cost price (CP)The amount paid to buy or produce an item.

Selling price (SP)The amount received when selling the item.

ProfitSP $-$ CP, when SP > CP. Positive earnings.

LossCP $-$ SP, when SP < CP. Negative outcome.

Break-evenWhen SP $=$ CP. Neither profit nor loss.

Marked priceThe displayed price — often discounted to give SP.

Spot the Trap

heads-up

Wrong: "Profit $= $ CP $-$ SP" — NO. Profit is SP minus CP (selling minus cost).

Right: Profit = SP − CP. Loss = CP − SP.

Wrong: "I bought for $\$200$ and sold for $\$175$, profit $= \$25$" — NO. SP $<$ CP means LOSS of $\$25$.

Right: You SOLD for less than you bought. That's a loss of $\$25$.

Profit and Loss in Practice

+5 XP

Most everyday buying-and-selling problems involve identifying CP and SP, then subtracting.

A market stall buys a tray of mangoes for $\$60$ (CP) and sells the whole tray for $\$84$ (SP). Profit $= 84 - 60 = \$24$. Conversely, if they sold for $\$48$ instead (CP $\$60 >$ SP $\$48$), they'd make a loss of $\$12$. Notice profit and loss are reported as positive numbers, with the word telling you direction.

Profit (or Loss) $= |$SP $-$ CP$|$, sign tells which

Identify CP

What did you PAY (or what did it cost to make)?

Identify SP

What did you RECEIVE?

Compare

SP $>$ CP? Profit. Otherwise, loss.

Multiple Items and Total Profit

+5 XP

Selling many items at once? Just multiply, then subtract.

A baker makes 100 loaves at a CP of $\$2$ each ($\$200$ total). They sell 80 loaves at $\$3.50$ each ($\$280$). The other 20 loaves go stale (sold for $\$0$). Total SP $= \$280$. Total CP $= \$200$. Profit $= 280 - 200 = \$80$. Even with waste, they profited.

Total Profit $= $ Total SP $-$ Total CP

Total it up

Sum ALL costs and ALL revenue first.

Wastage counts as cost

Unsold stock = unrecovered cost.

One subtraction at the end

Don't per-item — just totals.

Watch Me Solve It · 3 examples

Watch Me Solve It · The phone

+15 XP per step

PROBLEM

You buy a phone for $\$200$ and sell it for $\$175$. Profit or loss? How much?

1

Identify CP and SP

CP $= \$200$, SP $= \$175$

You paid $\$200$; got $\$175$ back.
2

Compare

SP $<$ CP $\to$ Loss

You took home less than you spent.
3

Compute loss

Loss $= 200 - 175 = \$25$

Always a positive amount, “loss” tells direction.

Answer$\$25$ loss

Watch Me Solve It · Mango stall

+15 XP per step

PROBLEM

A stall buys a box of mangoes for $\$48$ and sells them for $\$72$. What is the profit?

1

CP and SP

CP $= \$48$, SP $= \$72$

Paid 48, sold for 72.
2

SP $>$ CP

Yes — profit!

Profit-style situation.
3

Compute

$72 - 48 = \$24$

Total profit.

Answer$\$24$ profit

Watch Me Solve It · Multiple items

+15 XP per step

PROBLEM

You buy 12 books at $\$5$ each and sell 10 of them at $\$8$ each. The other 2 you lose. Total profit?

1

Total CP

$12 \times 5 = \$60$

All 12 books cost something.
2

Total SP

$10 \times 8 + 2 \times 0 = \$80$

You only sold 10; lost 2.
3

Profit

$80 - 60 = \$20$

Even after losing 2 books, you profited.

Answer$\$20$ profit

Common Pitfalls

heads-up

Swapping CP and SP

Calling the selling price the cost price.

Fix: CP = what you PAID. SP = what you RECEIVED.

Reporting a negative profit

Saying “profit of $-\$25$” instead of “loss of $\$25$”.

Fix: Use words. Profit or loss + dollar amount.

Forgetting unsold items

Only counting CP of items actually sold.

Fix: CP = total cost of EVERYTHING bought, not just sold.

Copy Into Your Books

Profit

Profit = SP − CP
SP > CP
You made money

Loss

Loss = CP − SP
SP < CP
You lost money

Break-even

SP = CP
Neither profit nor loss
Zero gain

Multiple items

Total CP = sum of all costs
Total SP = sum of all revenue
Profit = Total SP − Total CP

How are you completing this lesson?

Brain Trainer · 4 problems

Brain Trainer · Profit and Loss

4 problems

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

1 CP $\$30$, SP $\$45$. Profit?

$45 - 30 = \$15$.$\$15$ profit
2 CP $\$120$, SP $\$90$. Outcome?

$120 - 90 = \$30$ loss.$\$30$ loss
3 Buy 5 books at $\$4$ each, sell all at $\$6$ each. Profit?

CP $= 20$, SP $= 30$. $30 - 20 = \$10$.$\$10$ profit
4 CP $\$80$. Sold at break-even. SP?

SP $= $ CP $= \$80$$\$80$

Complete in your workbook.

Quick Check · 5 questions

A bike is bought for $\$300$ and sold for $\$450$. The profit is:

+10 XP

A jacket cost $\$80$ and sold for $\$65$. The outcome is:

+10 XP

A baker buys flour for $\$50$, makes 20 cakes, sells 18 at $\$5$. Total profit?

+10 XP

Break-even means:

+10 XP

You sell at $\$240$ for a $\$60$ profit. Cost price was:

+10 XP

Show Your Working · 3 questions

Show Your Working

9 marks total

Apply Medium 3 MARKS

Q6. Calculate profit or loss (state which): (a) CP $\$540$, SP $\$690$; (b) CP $\$1250$, SP $\$950$; (c) CP $\$320$, SP $\$320$.

Answer in your workbook.

Understand Easy 2 MARKS

Q7. A trader buys 30 phones at $\$120$ each and sells all 30 at $\$150$ each. What is the total profit?

Answer in your workbook.

Reason Hard 4 MARKS

Q8. A flower seller buys 200 bouquets at $\$4$ each. They sell 150 at $\$10$, and 30 at a discount of $\$6$. The remaining 20 wilt and are thrown out. (a) Calculate total CP. (b) Calculate total SP. (c) Determine the total profit or loss. (d) Comment on the impact of the 20 wilted bouquets on the overall outcome.

Answer in your workbook.

Comprehensive Answers

Quick Check

1. C — $\$150$ profit.

2. B — $\$15$ loss.

3. A — $\$40$ profit.

4. C — SP = CP.

5. A — $\$180$.

Show Your Working Model Answers

Q6 (3 marks): (a) $690 - 540 = \$150$ profit [1]. (b) $1250 - 950 = \$300$ loss [1]. (c) $320 - 320 = \$0$, break-even [1].

Q7 (2 marks): Total CP $= 30 \times 120 = \$3600$. Total SP $= 30 \times 150 = \$4500$ [1]. Profit $= 4500 - 3600 = \$900$ [1].

Q8 (4 marks): (a) Total CP $= 200 \times 4 = \$800$ [1]. (b) Total SP $= 150 \times 10 + 30 \times 6 + 20 \times 0 = 1500 + 180 + 0 = \$1680$ [1]. (c) Profit $= 1680 - 800 = \$880$ profit [1]. (d) The 20 wilted bouquets cost the seller $\$80$ (their CP) in unrecovered cost — without that wastage, profit would have been $\$960$ [1].

Stretch Challenge · +25 XP, +10 coins

The Re-Sale Game

A trader buys a vintage guitar for $\$1500$. They spend $\$200$ restoring it. They list it for $\$2400$ but accept an offer of $\$2100$ after one week. (a) What is the total CP? (b) What is the SP? (c) What is the profit or loss? (d) Was the negotiation worthwhile, given the alternative would have been to sit on it unsold?

Reveal solution

(a) Total CP $= 1500 + 200 = \$1700$ (cost of buying + restoring). (b) SP $= \$2100$. (c) Profit $= 2100 - 1700 = \$400$. (d) Yes — accepting the $\$2100$ offer crystallised a $\$400$ profit. Holding out for $\$2400$ (extra $\$300$) risked a longer wait, possible price drop, and tied-up cash; locking in profit is often the right call.

Quick Review

CP and SP

You buy at CP, sell at SP

Profit

SP > CP

Loss

SP < CP

Break-even

SP = CP

Total it

Sum CP and SP separately

Word + dollars

State direction + amount

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