P6 Mathematics - Term II

Topic 5: Fractions

Lesson 5: Loss and Profit

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Define profit and loss in business transactions
• Calculate profit and loss from buying and selling prices
• Find profit percentage and loss percentage
• Solve word problems involving profit and loss
• Apply these concepts to real-life business in Uganda

Let's Think About Business

Questions:

• Who has bought something from a shop or market?
• Why do shopkeepers sell items?
• Do they sell at the same price they bought?
• What happens when they sell for more? For less?

Key Business Terms

Cost Price (CP):
The price at which an item is bought

Selling Price (SP):
The price at which an item is sold

These are the foundation of all profit and loss calculations!

What is Profit?

Profit:
Money gained when selling price is MORE than cost price

Simple example:

• Buy a bag of sugar for 10,000 shillings (CP)
• Sell it for 12,000 shillings (SP)
• Made profit because SP > CP!

What is Loss?

Loss:
Money lost when selling price is LESS than cost price

Simple example:

• Buy a chicken for 15,000 shillings (CP)
• Sell it for 13,000 shillings (SP)
• Made loss because SP < CP

The Three Situations

If SP > CP: There is PROFIT

If SP < CP: There is LOSS

If SP = CP: NO profit, NO loss
(Break even)

Formula for Profit

When SP > CP:

Profit = Selling Price - Cost Price

Profit = SP - CP

Always subtract the smaller from the larger!

Example 1: Calculating Profit

Problem:
A shopkeeper buys a radio for 50,000 shillings.
He sells it for 65,000 shillings.
Calculate the profit.

Solution:
CP = 50,000, SP = 65,000
Profit = SP - CP = 65,000 - 50,000 = 15,000

Answer: 15,000 shillings profit

Example 2: Another Profit

Problem:
Akello buys mangoes for 20,000 shillings.
She sells them for 28,000 shillings.
Calculate her profit.

Solution:
CP = 20,000, SP = 28,000
Profit = 28,000 - 20,000 = 8,000

Answer: 8,000 shillings profit

Formula for Loss

When CP > SP:

Loss = Cost Price - Selling Price

Loss = CP - SP

Cost is bigger, so subtract selling from cost!

Example 1: Calculating Loss

Problem:
A trader buys matooke for 30,000 shillings.
She sells it for 25,000 shillings.
Calculate the loss.

Solution:
CP = 30,000, SP = 25,000
Loss = CP - SP = 30,000 - 25,000 = 5,000

Answer: 5,000 shillings loss

Example 2: Another Loss

Problem:
Okello buys a bicycle for 200,000 shillings.
He sells it for 180,000 shillings.
Calculate his loss.

Solution:
CP = 200,000, SP = 180,000
Loss = 200,000 - 180,000 = 20,000

Answer: 20,000 shillings loss

Your Turn: Practice

Solve in your exercise book:

a) CP = 40,000, SP = 50,000. Find profit.
b) CP = 60,000, SP = 55,000. Find loss.
c) CP = 15,000, SP = 18,000. Profit or loss? How much?

Show all your working!

Why Calculate Percentage?

Question: Is a profit of 10,000 shillings good?

It depends!

• If you started with 20,000 → That's great! (50% profit)
• If you started with 200,000 → That's not much (5% profit)

Percentages help us compare fairly!

Formula for Profit Percentage

How to find profit as a percentage:

Profit % = (Profit / Cost Price) × 100

Profit % = (Profit / CP) × 100

Always divide by cost price - what you started with!

Example 1: Profit Percentage

Problem:
Buy items for 50,000 shillings (CP)
Sell for 60,000 shillings (SP)
Calculate profit percentage.

Step 1: Profit = 60,000 - 50,000 = 10,000

Step 2: Profit % = (10,000 / 50,000) × 100 = 20%

Example 2: Profit Percentage

Problem:
Okello buys a goat for 80,000 shillings
Sells it for 100,000 shillings
Calculate profit percentage.

Step 1: Profit = 100,000 - 80,000 = 20,000

Step 2: Profit % = (20,000 / 80,000) × 100 = 25%

Formula for Loss Percentage

How to find loss as a percentage:

Loss % = (Loss / Cost Price) × 100

Loss % = (Loss / CP) × 100

Same pattern - divide by cost price!

Example 1: Loss Percentage

Problem:
Buy shirts for 40,000 shillings (CP)
Sell for 32,000 shillings (SP)
Calculate loss percentage.

Step 1: Loss = 40,000 - 32,000 = 8,000

Step 2: Loss % = (8,000 / 40,000) × 100 = 20%

Example 2: Loss Percentage

Problem:
Trader buys beans for 60,000 shillings
Sells them for 54,000 shillings
Calculate loss percentage.

Step 1: Loss = 60,000 - 54,000 = 6,000

Step 2: Loss % = (6,000 / 60,000) × 100 = 10%

Your Turn: Percentage Practice

Solve in your exercise book:

CP = 50,000, SP = 65,000

Find:
a) Profit amount
b) Profit percentage

Show both steps clearly!

Real-Life Application 1

Sugar Business:
A trader buys sugar for 80,000 shillings
Sells it for 100,000 shillings

Results:
Profit = 20,000 shillings
Profit % = 25%

This is a successful business!

Real-Life Application 2

Phone Sale:
Okello bought a phone for 200,000 shillings
Sold it for 160,000 shillings (needed money)

Results:
Loss = 40,000 shillings
Loss % = 20%

Sometimes we have to accept losses.

Summary: Key Formulas

Profit = SP - CP (when SP > CP)

Loss = CP - SP (when CP > SP)

Profit % = (Profit / CP) × 100

Loss % = (Loss / CP) × 100

Why Business People Need This

Making decisions:

• Is this a good deal?
• Should I sell now or wait?
• Am I pricing things correctly?

Comparing businesses:

• Which product is more profitable?
• Where should I invest?

Quick Assessment

Answer in your exercise book:

1. CP = 30,000, SP = 40,000. Find profit.
2. CP = 50,000, SP = 45,000. Find loss.
3. A trader buys sugar for 80,000 and sells for 100,000. Find profit and profit %.
4. Akello bought a dress for 25,000, sold for 30,000. Find profit %.

Challenge Problem

Two-part challenge:

Part 1: Matooke costs 60,000, sells for 75,000.
Find profit and profit %.

Part 2: If profit % was 30% instead, what would selling price be?

Homework: Parts A and B

Part A: Calculating Profit (3 problems)

1. CP = 20,000, SP = 28,000
2. Oranges bought for 15,000, sold for 21,000
3. Books bought for 40,000, sold for 52,000

Part B: Calculating Loss (3 problems)
4. CP = 35,000, SP = 30,000
5. Radio bought for 50,000, sold for 42,000
6. Bicycle bought for 180,000, sold for 150,000

Homework: Parts C and D

Part C: Percentages (4 problems)
7. CP = 40,000, SP = 50,000. Find profit %.
8. CP = 80,000, SP = 64,000. Find loss %.
9. Matooke: CP = 60,000, SP = 75,000. Find profit and profit %.
10. Sugar: CP = 100,000, SP = 90,000. Find loss and loss %.

Part D: Word Problems (2 problems)

Looking Ahead

Next Lesson:
We will learn about simple interest

Connection:
Interest is like profit on money you save or lend!
Same percentage calculations!

Key Takeaways

Identify first: Is it profit or loss?

Calculate amount: Use subtraction

Calculate percentage: Divide by CP, multiply by 100

Two steps: Amount first, then percentage

Always check: Does my answer make sense?