Class 8 - Profit and Loss

Profit and loss is a simple but important concept in mathematics that helps us understand whether we are making money or losing it when we buy and sell something. In simple terms, profit and loss help you keep track of money showing whether you’re gaining or losing in any transaction. Understanding this concept makes it easier to make smarter financial decisions in real life.

Table of Contents

• Profit and Loss Basic Concepts
• Profit and Loss Formulas
• Solved Problems On Profit And Loss
• Practice Questions On Profit And Loss

Profit and Loss Basic Concepts

Let us learn profit and loss concepts in maths. It is well explained in terms of cost price and selling price.

What is Cost Price?

Cost Price (CP) is simply the amount you pay to buy something. It's what the item costs you.

What is Selling Price?

Selling Price (SP) is the amount you receive when you sell something. It's what you get paid.

What is Profit?

Profit happens when you sell something for MORE than what you paid for it. You're making money.

• Profit = Selling Price − Cost Price (when SP > CP)

What is Loss?

Loss happens when you sell something for LESS than what you paid for it. You're losing money

• Loss = Cost Price − Selling Price (when CP > SP)

Key point to remember: Loss happens when Selling Price is LESS than Cost Price.

Here's a simple way to remember:

• If SP > CP:  You made PROFIT.
• If SP < CP: You faced LOSS.
• If SP = CP:  No profit, no loss.

What is Profit Percentage?

Sometimes we don't just want to know the profit amount. We want to know how much profit we made compared to what we spent.

For example: making ₹10 profit on a ₹20 item is amazing (that's 50%), but making ₹10 profit on a ₹1000 item is barely anything (just 1%).

What is Loss Percentage?

Similarly, loss percentage tells you how much money you lost for every ₹100 you spent.

Discount − A Special Concept

You've probably seen sale signs saying "50% OFF" or "Buy 1 Get 1 Free." That's discount.

What is Marked Price?

Marked Price (MP) is the price tag you see on an item in a shop. It's the original price before any discount.

What is Discount?

Discount is the reduction in marked price. It's how much the shopkeeper cuts from the original price.

Profit and Loss Formulas

Now let us find the profit formula and loss formula.

• The profit or gain is equal to the selling price minus the cost price.

• Loss is equal to the cost price minus the selling price.

Profit or Gain = Selling price − Cost Price

Loss = Cost Price − Selling Price

The formula for the profit and loss percentage is:

Profit percentage (P%) = (Profit /Cost Price) x 100

Loss percentage (L%) = (Loss / Cost price) x 100

Quick Formula Summary Table

Solved Problems On Profit And Loss

Problem 1: Basic Profit Calculation

Question: Rohan bought a bicycle for ₹3,500 and sold it for ₹4,200. Find his profit and profit percentage.

Solution:

• Cost Price (CP) = ₹3,500

• Selling Price (SP) = ₹4,200

Step 1: Check if there's a profit or a loss

SP (₹4,200) > CP (₹3,500), So there's profit

Step 2: Calculate profit

Profit = SP − CP

Profit = 4,200 − 3,500

Profit = ₹700

Step 3: Calculate profit percentage

Profit% = (Profit/CP) × 100

Profit% = (700/3,500) × 100

Profit% = (1/5) × 100

Profit% = 20%

Answer: Rohan made a profit of ₹700, which is 20% profit.

Problem 2: Finding Selling Price

Question: A shopkeeper bought a chair for ₹1,200. He wants to make 15% profit. At what price should he sell it?

Solution:

• CP = ₹1,200

• Profit% = 15%

• SP =?

Method 1 (Using formula):

SP = CP × (100 + Profit%)/100

SP = 1,200 × (100 + 15)/100

SP = 1,200 × 115/100

SP = 1,200 × 1.15

SP = ₹1,380

Method 2 (Step by step):

Profit = 15% of ₹1,200

Profit = (15/100) × 1,200

Profit = ₹180

SP = CP + Profit

SP = 1,200 + 180

SP = ₹1,380

Answer: The shopkeeper should sell the chair for ₹1,380.

Problem 3: Finding Cost Price

Question: Ravi sold his phone for ₹8,400 and made a loss of 20%. What was the cost price of the phone?

Solution:

• SP = ₹8,400

• Loss% = 20%

• CP =?

Using formula:

CP = [SP × 100]/(100 − Loss%)

CP = [8,400 × 100]/(100 − 20)

CP = [8,400 × 100]/80

CP = 8,40,000/80

CP = ₹10,500

Let's check: If CP = ₹10,500 and loss is 20%

Loss = 20% of 10,500 = ₹2,100

SP = CP − Loss = 10,500 − 2,100 = ₹8,400

Answer: The cost price of the phone was ₹10,500.

Problem 4: Discount Problem

Question: A shirt has a marked price of ₹800. The shop offers a 25% discount. Find the selling price and the discount amount.

Solution:

• Marked Price (MP) = ₹800

• Discount% = 25%

Step 1: Calculate discount amount

Discount = 25% of ₹800

Discount = (25/100) × 800

Discount = ₹200

Step 2: Calculate selling price

SP = MP − Discount

SP = 800 − 200

SP = ₹600

Quick method:

SP = MP × (100 − Discount%)/100

SP = 800 × 75/100

SP = ₹600

Answer: Discount amount is ₹200 and selling price is ₹600.

Problem 5: Combined Profit and Discount

Question: A shopkeeper marks a watch 40% above the cost price. He then gives a 20% discount. Find his profit percentage.

Solution:

• Let CP = ₹100 (taking base value)

• MP = 40% above CP

• Discount = 20%

Step 1: Find Marked Price

MP = CP + 40% of CP

MP = 100 + 40

MP = ₹140

Step 2: Find Selling Price after discount

Discount = 20% of MP

Discount = 20% of 140 = ₹28

SP = MP − Discount

SP = 140 − 28

SP = ₹112

Step 3: Find Profit and Profit%

CP = ₹100, SP = ₹112

Profit = SP − CP = 112 − 100 = ₹12

Profit% = (12/100) × 100 = 12%

Answer: The shopkeeper makes 12% profit.

Practice Questions On Profit And Loss

1. A book costs ₹180 and is sold for ₹210. Find the profit percentage.

2. A shopkeeper sells a toy for ₹450 and makes a loss of 10%. What was the cost price?

3. Calculate the selling price if CP = ₹600 and profit is 25%.

4. A shirt marked at ₹1,200 is sold at 15% discount. Find the selling price.

5: A dishonest shopkeeper claims to sell at cost price but uses a 900g weight instead of 1 kg. Find his profit percentage.