Understand the meaning of Cost Price (CP) and Selling Price (SP)
Determine when there is a profit and when there is a loss
Calculate profit and loss amounts
Calculate profit percentage and loss percentage
Find Selling Price when Cost Price and profit/loss are given
Understand Marked Price (MRP) and Discount
Calculate discount amount and selling price after discount
Solve word problems involving profit, loss, and discount in real-life Indian contexts
Introduction — Buying and Selling in Everyday Life
Every day, people buy and sell things around us. Your parents buy vegetables from the sabzi mandi, clothes from a shop, and books from a bookstore. Shopkeepers buy goods from wholesalers at one price and sell them to us at another price. When a shopkeeper sells something for more than what he paid, he makes a profit. When he sells for less than what he paid, he suffers a loss.
During Diwali sales, Durga Puja offers, and Republic Day discounts, shops give us discounts — they reduce the price so we pay less than the price written on the tag. In this chapter, we will learn how to calculate profit, loss, and discount using simple formulas.
Key Terms — Cost Price, Selling Price, Profit, and Loss
Before we start calculating, let us understand the important terms:
Term
Meaning
Example
Cost Price (CP)
The price at which a shopkeeper buys an item (also called the purchase price)
Ravi buys a cricket bat for ₹800. His CP = ₹800
Selling Price (SP)
The price at which a shopkeeper sells an item to a customer
Ravi sells the bat for ₹950. His SP = ₹950
Profit
The extra money earned when SP is more than CP
Ravi's profit = ₹950 − ₹800 = ₹150
Loss
The money lost when SP is less than CP
If Ravi sells the bat for ₹700, loss = ₹800 − ₹700 = ₹100
Image needed: A flowchart/diagram showing the relationship between CP, SP, Profit and Loss. Show two paths: one where SP > CP (leading to Profit) and one where SP < CP (leading to Loss). Use arrows and colour coding (green for profit, red for loss). Style: Clean flat illustration, child-friendly, colourful flowchart Size: 700×400px
Think About It: When Meena's mother buys mangoes at ₹200 per kg from the market and sells them at the same price (₹200 per kg) to her neighbour, there is no profit and no loss. This happens when CP = SP.
When is it Profit? When is it Loss?
The simple rule is:
The Golden Rule of Profit and Loss
If SP > CP → There is a Profit (the seller earns extra money)
If SP < CP → There is a Loss (the seller loses money)
If SP = CP → There is No Profit, No Loss
Example 1: Arjun buys a football for ₹450 and sells it for ₹520.
CP = ₹450, SP = ₹520. Since SP > CP → Profit!
Example 2: Priya buys a second-hand bicycle for ₹2,500 and sells it for ₹2,100.
CP = ₹2,500, SP = ₹2,100. Since SP < CP → Loss!
Example 3: Dhruv buys a notebook for ₹60 and sells it to his friend for ₹60.
CP = ₹60, SP = ₹60. Since SP = CP → No Profit, No Loss!
Image needed: Three scenarios shown side by side: (1) Happy shopkeeper with green arrow up = Profit (SP > CP), (2) Sad shopkeeper with red arrow down = Loss (SP < CP), (3) Neutral shopkeeper with equals sign = No profit no loss (SP = CP). Each with a simple price tag illustration. Style: Cartoon-style, child-friendly, colourful, Indian shopkeeper character Size: 750×350px
Calculating Profit and Loss
Now let us learn the formulas to calculate the exact amount of profit or loss:
Formulas
Profit = Selling Price − Cost Price (SP − CP)
Loss = Cost Price − Selling Price (CP − SP)
Worked Examples — Finding Profit
Example 1: A shopkeeper buys a school bag for ₹350 and sells it for ₹480. Find his profit.
Given: CP = ₹350, SP = ₹480 Since SP > CP, there is a profit.
Profit = SP − CP = ₹480 − ₹350 = ₹130
The shopkeeper makes a profit of ₹130.
Example 2: Akriti buys a dozen bananas for ₹60 and sells them for ₹84. What is her profit?
Just knowing the profit or loss amount is not always enough. We need to know how much profit or loss was made compared to the cost price. This is expressed as a percentage.
Think of it this way: If a shopkeeper makes ₹100 profit on an item that cost ₹200, that is a 50% profit (very good!). But if he makes ₹100 profit on an item that cost ₹10,000, that is only 1% profit (very little!).
Formulas for Profit% and Loss%
Profit % = (Profit ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100
Important: Profit% and Loss% are always calculated on the Cost Price (CP), not on SP!
Worked Examples — Profit Percentage
Example 1: A shopkeeper buys a chair for ₹500 and sells it for ₹600. Find the profit percentage.
Example 4: Priya bought a dress for ₹1,500 and sold it at a 10% loss. Find the selling price.
Step 1: Loss amount = 10% of CP = (10 ÷ 100) × 1500 = ₹150 Step 2: SP = CP − Loss = ₹1,500 − ₹150 = ₹1,350
What is Discount?
When you go to a shop, you see a price printed on every product — this is called the Marked Price (MRP) or the Maximum Retail Price. During sales and festivals, shopkeepers reduce this price to attract customers. The amount reduced from the Marked Price is called the Discount.
Key Terms
Marked Price (MRP) = The price printed on the tag or label of the product
Discount = The reduction (amount less) offered by the shopkeeper on the MRP
Selling Price (SP) = The price the customer actually pays after discount
Image needed: A price tag illustration showing MRP ₹500 crossed out with a red line, and a new discounted price ₹400 shown below. A "20% OFF" starburst badge. Labels pointing to MRP, Discount amount (₹100), and final SP (₹400). Style: Clean flat illustration, shopping/retail theme, colourful, child-friendly Size: 600×400px
Think About It: Have you seen "FLAT 50% OFF" banners during Diwali or Durga Puja sales? This means the shopkeeper is giving a discount of 50% on the MRP. So if a shirt's MRP is ₹1,000, you only pay ₹500!
Calculating Discount
Let us learn how to calculate the discount amount and the price the customer pays.
Finding Discount Amount and SP (given MRP and Discount%)
Example 1: A shirt has an MRP of ₹800. The shop is giving a 25% discount. Find the discount amount and the selling price.
A shopkeeper first buys an item at the Cost Price (CP). Then he puts a Marked Price (MRP) on it — this is usually higher than CP. During sales, he gives a discount and sells at the Selling Price (SP). Even after giving a discount, he can still make a profit if the SP is more than CP!
The Full Chain
Shopkeeper buys at CP
Shopkeeper marks the item at MRP (MRP > CP usually)
Shopkeeper gives Discount on MRP
Customer pays SP = MRP − Discount
If SP > CP → Shopkeeper still makes Profit!
If SP < CP → Shopkeeper makes a Loss (clearance sale)
Example: A shopkeeper buys a jacket for ₹1,000 (CP). He marks it at ₹1,600 (MRP). During winter sale, he gives 25% discount.
Even after giving 25% discount, the shopkeeper still makes 20% profit!
Image needed: A visual showing the relationship: CP (₹1,000) → MRP (₹1,600) → Discount (₹400) → SP (₹1,200) → Profit (₹200). Use a horizontal bar chart or step diagram with amounts marked. Show CP, MRP, SP on a number line or stacked bars. Style: Infographic, step-by-step visual, colourful bars, child-friendly Size: 750×350px
Word Problems — Real-Life Situations
Let us solve some problems based on real-life buying and selling in India:
Problem 1: A fruit seller buys 10 kg of mangoes for ₹1,500 and sells them for ₹180 per kg. Find his profit and profit%.
CP of 10 kg = ₹1,500
SP of 10 kg = 10 × ₹180 = ₹1,800
Profit = SP − CP = ₹1,800 − ₹1,500 = ₹300
Profit% = (300 ÷ 1500) × 100 = 20%
Problem 2: During a book fair, Dhruv buys a story book for ₹250. He reads it and sells it to his classmate for ₹200. Find the loss%.
Problem 3: A shopkeeper buys 50 notebooks at ₹30 each. He sells 40 of them at ₹40 each and the remaining 10 at ₹25 each (damaged). Find his overall profit or loss.
Problem 4: A TV has an MRP of ₹30,000. During Republic Day sale, a 20% discount is offered. The shopkeeper had bought the TV for ₹22,000. Find: (a) Discount amount, (b) SP, (c) Profit or Loss, (d) Profit or Loss %.
2. If a shopkeeper buys at ₹1,000 and sells at ₹800, his loss is ₹
3. Profit % is always calculated on (CP / SP / MRP)
4. Discount % is calculated on (CP / SP / MRP)
5. If MRP = ₹1,000 and discount = 30%, then SP = ₹
F. True or False:
1. If SP > CP, the seller makes a loss.
2. Profit% = (Profit ÷ SP) × 100.
3. Discount is always calculated on the Marked Price.
4. A shopkeeper can make profit even after giving a discount.
5. If CP = SP, there is a loss.
G. Choose the correct answer (MCQ):
1. A pen is bought for ₹20 and sold for ₹25. The profit % is:
a) 20%b) 25%c) 5%d) 50%
2. MRP of a bag is ₹500. If 20% discount is given, the SP is:
a) ₹480b) ₹400c) ₹100d) ₹600
3. CP = ₹800, Loss = 25%. The SP is:
a) ₹200b) ₹600c) ₹1,000d) ₹575
4. If SP = CP, then:
a) Profit = 100%b) Loss = 100%c) No profit, no lossd) Discount = 0%
H. Word Problems:
1. A shopkeeper in Chandni Chowk buys 20 kg of rice at ₹50 per kg and sells it at ₹62 per kg. Find his total profit and profit%.
2. During Durga Puja sale, a saree with MRP ₹2,400 is sold at 30% discount. Find the discount amount and the price Meena pays.
3. Arjun buys a bicycle for ₹5,000 and spends ₹500 on repairs. He then sells it for ₹6,050. Find his profit and profit%. (Hint: Total CP = Purchase price + Repair cost)
4. A toy shop gives 15% discount on all toys. If a toy car has an MRP of ₹840 and the shopkeeper bought it for ₹600, find: (a) SP after discount, (b) Profit or Loss, (c) Profit%.
5. Priya bought 5 kg of apples at ₹200 per kg. She sold 3 kg at ₹250 per kg and the remaining 2 kg (which had become overripe) at ₹120 per kg. Find her overall profit or loss.
6. An online store has a Diwali sale: "FLAT 40% OFF on everything!" Ravi wants to buy a cricket kit with MRP ₹3,500. How much will he pay? If the store bought the kit for ₹1,800, what is the store's profit%?
Activity — My Mini Shop!
Imagine you are a shopkeeper! You buy these items at the given Cost Prices. Now decide:
What MRP (Marked Price) will you put on each item?
What discount (%) will you offer during a sale?
Calculate your final SP and profit for each item.
Item
CP (Your Cost)
MRP (You Decide)
Discount % (You Decide)
Discount Amount
SP (Customer Pays)
Profit
Notebook
₹40
Water bottle
₹120
Pencil box
₹80
Story book
₹150
School bag
₹350
Challenge: Can you give a discount and still make at least 10% profit on every item? Try it!
Want to review the lesson again?
Mathematics
Profit, Loss and Discount
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Understand Cost Price (CP) and Selling Price (SP)
Calculate profit and loss amounts
Calculate profit% and loss%
Understand Marked Price (MRP) and Discount
Calculate discount amount and SP after discount
Solve word problems involving profit, loss, and discount
Introduction
Every day, shopkeepers buy goods at one price and sell at another. When SP > CP, they make a profit. When SP < CP, they suffer a loss. During Diwali sales and festivals, shops offer discounts (reductions on MRP). In this chapter, we learn to calculate profit, loss, and discount.
The price printed on a product is the Marked Price (MRP). During sales, shopkeepers reduce this price. The reduction is called Discount. The price customer pays is SP = MRP − Discount.
The Full Chain:
Shopkeeper buys at CP → Marks at MRP → Gives Discount → Sells at SP = MRP − Discount
If SP > CP → Still makes Profit (even after discount!)
Key Points:
• Profit = SP − CP | Loss = CP − SP
• Profit% and Loss% calculated on CP
• Discount% calculated on MRP
• SP = CP + Profit or SP = CP − Loss
• SP = MRP − Discount
• Shopkeeper can give discount and still earn profit if SP > CP
• No profit, no loss → SP = CP