PROFIT AND LOSS

Definition

Profit and Loss is a topic in commercial arithmetic that deals with the buying and selling of goods or services.

A Profit occurs when the Selling Price (SP) is greater than the Cost Price (CP), while a Loss occurs when the Selling Price (SP) is less than the Cost Price (CP).

Profit and Loss are widely used in business, trade, accounting, finance, economics, entrepreneurship, and everyday buying and selling activities.


1. Cost Price (CP)

Definition

The Cost Price (CP) is the amount of money paid to purchase or produce an item before it is sold.

Examples

(i) A bicycle bought for $180 has a cost price of $180.

(ii) A bag purchased for $45 has a cost price of $45.

(iii) A television bought for $650 has a cost price of $650.


2. Selling Price (SP)

Definition

The Selling Price (SP) is the amount of money received after selling an item.

Examples

(i) A bicycle sold for $220 has a selling price of $220.

(ii) A bag sold for $55 has a selling price of $55.

(iii) A television sold for $720 has a selling price of $720.


3. Profit

Definition

A Profit is made when the Selling Price (SP) is greater than the Cost Price (CP).

Profit = Selling Price − Cost Price

Example

Cost Price = $150

Selling Price = $190

Profit = 190 − 150 = $40


4. Loss

Definition

A Loss occurs when the Selling Price (SP) is less than the Cost Price (CP).

Loss = Cost Price − Selling Price

Example

Cost Price = $250

Selling Price = $210

Loss = 250 − 210 = $40


5. Percentage Profit

Percentage Profit is the profit made expressed as a percentage of the original cost price.

Percentage Profit Formula:

We get the percentage profit using the formula below:

Percentage Profit = Profit Cost Price × 100%

In order to get profit, we subtract the cost price from the selling price;

Profit = Selling Price - Cost Price


Example

A trader buys a bicycle for $250 and sells it for $320. Find the percentage profit of the bicycle.

solution :

Step 1:Get the Profit

Cost Price = $250

Selling Price = $320

Profit = Selling Price - Cost Price

Profit = $320 - $250

Profit = $70

Since we have Profit, we can get the percentage profit by using the formula:

Percentage Profit = Profit Cost Price × 100%

Step 2: Substitute the values in the formula.

Percentage Profit = $70 $250 × 100%

Percentage Profit = 28%

6. Percentage Loss

Percentage Loss is the loss incurred expressed as a percentage of the original cost price.

Percentage Loss Formula:

We get the percentage loss using the formula below:

Percentage Loss = Loss Cost Price × 100%

In order to get loss, we subtract the selling price from the cost price;

Loss = Cost Price - Selling Price


Example

A phone is bought for $600 but sold for $540, find the percentage loss of the phone.

solution :

Step 1:Get the Loss

Cost Price = $600

Selling Price = $540

Loss = Cost Price - Selling Price

Loss = $600 - $540

Loss = $60

Since we have Loss, we can get the percentage loss by using the formula:

Percentage Loss = Loss Cost Price × 100%

Step 2: Substitute the values in the formula.

Percentage Loss = $60 $600 × 100%

Percentage Loss = 10%


7. Worked Examples

Example 1

A trader bought a chair for $120 and sold it for $165. Find the profit.

Solution

Step 1: Identify the Cost Price and Selling Price.

CP = $120

SP = $165

Step 2: Apply the profit formula.

Profit = SP − CP

= 165 − 120

= 45

Final Answer: Profit = $45


Example 2

A laptop was bought for $850 and sold for $780. Find the loss.

Solution

Step 1: Identify the Cost Price and Selling Price.

CP = $850

SP = $780

Step 2: Apply the loss formula.

Loss = CP − SP

= 850 − 780

= 70

Final Answer: Loss = $70


Example 3

A merchant bought a table for $400 and sold it for $500. Find the percentage profit.

Solution

Step 1: Find the profit.

Profit = 500 − 400 = 100

Step 2: Apply the profit percentage formula.

Profit % = (100 ÷ 400) × 100%

= 0.25 × 100%

= 25%

Final Answer: percentage profit = 25%


Example 4

A phone was bought for $600 and sold for $510. Find the percentage loss.

Solution

Step 1: Find the loss.

Loss = 600 − 510 = 90

Step 2: Apply the loss percentage formula.

Loss % = (90 ÷ 600) × 100%

= 0.15 × 100%

= 15%

Final Answer: percentage loss = 15%


Example 5

A shopkeeper bought 40 bags of rice at $35 each and sold each bag for $42. Calculate the total profit.

Solution

Step 1: Find the profit on one bag.

Profit = 42 − 35 = 7

Step 2: Find the total profit.

Total Profit = 40 × 7

= 280

Final Answer: Total Profit = $280


Sample Questions

Attempt the following Questions:

(i) A trader bought a refrigerator for $850 and sold it for $1,020. Calculate the profit and the percentage profit.

(ii) A furniture dealer purchased a dining table for $640 but later sold it for $560. Determine the loss and the percentage loss.

(iii) A wholesaler bought 75 cartons of milk at $18 per carton and sold each carton for $22. Calculate the total profit made.

(iv) A laptop was sold for $1,080 after making a 20% profit. Find the cost price of the laptop.

(v) A shopkeeper bought a bicycle for $480. He wanted to make a profit of 25%. Determine the selling price of the bicycle.

Check The Answers Below:

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