Profit and Loss: Mastering the Basics of Business Math

Introduction

Imagine you bought a phone for $500 and sold it for $600. You just made a profit of $100! But what if you had to sell it for $450? That would be a loss of $50. Understanding profit and loss is essential in business, shopping, and even daily budgeting.

In this guide, you’ll learn:

What profit and loss mean
How to calculate profit, loss, and percentages
Real-life applications of profit and loss
Common mistakes and how to avoid them

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Understanding Profit and Loss

Profit and loss occur when the selling price (SP) and cost price (CP) of an item are different.

Cost Price (CP) – The price at which an item is bought.
Selling Price (SP) – The price at which an item is sold.

When Do You Make a Profit?

If SP > CP, the seller makes a profit.

Profit Formula:

Profit=SP−CP\text{Profit} = \text{SP} – \text{CP}Profit=SP−CP

Example:
A bike is bought for $400 and sold for $500.
Profit = $500 – $400 = $100

When Do You Incur a Loss?

If SP < CP, the seller incurs a loss.

Loss Formula:

Loss=CP−SP\text{Loss} = \text{CP} – \text{SP}Loss=CP−SP

Example:

A laptop is bought for $800 and sold for $750.
Loss = $800 – $750 = $50

Calculating Profit and Loss Percentage

Percentages help in comparing profit and loss easily.

Profit Percentage Formula

Profit %=(ProfitCP×100)%\text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}} \times 100\right) \%Profit %=(CPProfit×100)%

Example:

A table is bought for $200 and sold for $250.
Profit = $250 – $200 = $50
Profit % = (50 / 200) × 100 = 25%

Loss Percentage Formula

Loss %=(LossCP×100)%\text{Loss \%} = \left(\frac{\text{Loss}}{\text{CP}} \times 100\right) \%Loss %=(CPLoss×100)%

Example:
A jacket is bought for $150 and sold for $120.
Loss = $150 – $120 = $30
Loss % = (30 / 150) × 100 = 20%

Mark Price and Discounts: The Role of Price Tags

Businesses often increase the price (mark price) and then offer discounts.

Marked Price (MP) – The price before any discount.
Discount – A reduction in price to attract buyers.

Selling Price After Discount:

SP=MP−Discount\text{SP} = \text{MP} – \text{Discount}SP=MP−Discount

Example:

A TV has a marked price of $1,200. The store offers a 20% discount.

Discount Amount = (20/100) × 1200 = $240

Final Price = $1200 – $240 = $960

Breaking Even: No Profit, No Loss

If SP = CP, there is no profit and no loss.

Example:

A bookstore buys 100 books for $500 and sells all for $500. The seller neither gains nor loses money.

Why Is Profit and Loss Important?

Profit and loss calculations are crucial in many fields:

Business – Helps companies set prices and track earnings.
Investments – Determines financial growth or loss.
Retail Shopping – Helps buyers understand discounts and deals.
Personal Finance – Helps manage expenses and savings.

5 Common Mistakes in Profit and Loss Calculations

Forgetting to Use Cost Price in Percentage Calculations
Using Selling Price Instead of Marked Price for Discounts
Mixing Up Profit and Loss Formulas
Ignoring Discounts Before Calculating Profit or Loss
Forgetting to Convert Percentage to Decimal in Some Cases

5 Profit and Loss Practice Questions

A phone is bought for $700 and sold for $900. Find the profit and profit percentage.
A store buys shoes for $500 and sells them for $450. Calculate the loss and loss percentage.
A dress has a marked price of $2,000 and is sold after a 25% discount. Find the selling price.
A company spends $10,000 on manufacturing and sells the products for $12,000. Calculate the profit and profit %.
A car dealer buys a car for $15,000 and sells it at a loss of 5%. Find the selling price.