Learning Objectives
- Understand the meaning of Cost Price (CP) and Selling Price (SP).
- Learn when a shopkeeper makes a profit and when there is a loss.
- Calculate profit using the formula: Profit = SP - CP.
- Calculate loss using the formula: Loss = CP - SP.
Let Us Begin!
Ramesh runs a small stationery shop near a school in Pune. He buys a box of crayons from the market for Rs 40 and sells it to a student for Rs 55. He gets Rs 15 more than what he paid. This extra money is called profit.
One day, Ramesh buys a geometry box for Rs 80 but can only sell it for Rs 65. He gets Rs 15 less than what he paid. This is called a loss.
Let us learn how to find profit and loss step by step.
[Image: A shopkeeper at a stall with two scenarios — Left: "Cost Price ₹50, Selling Price ₹70 → Profit ₹20" with a happy face. Right: "Cost Price ₹80, Selling Price ₹60 → Loss ₹20" with a sad face. Title: "Profit and Loss"]
Step-by-Step Explanation
What is Cost Price (CP)?
The Cost Price is the amount a shopkeeper pays to buy an item. It is also called the buying price.
Example: Ramesh buys a notebook for Rs 25. The Cost Price (CP) = Rs 25.
What is Selling Price (SP)?
The Selling Price is the amount a shopkeeper receives when he sells the item to a customer.
Example: Ramesh sells the notebook for Rs 35. The Selling Price (SP) = Rs 35.
Think about it: The shopkeeper wants SP to be more than CP. Why? Because that is how he earns money!
When is There a Profit?
When the Selling Price is more than the Cost Price, the shopkeeper makes a profit.
Profit = SP - CP (when SP > CP)
When is There a Loss?
When the Selling Price is less than the Cost Price, the shopkeeper suffers a loss.
Loss = CP - SP (when CP > SP)
When is There No Profit and No Loss?
When the Selling Price is equal to the Cost Price, there is no profit and no loss.
Think about it: A fruit seller in Kolkata buys a dozen bananas for Rs 36 and sells them for Rs 36. Did she make a profit or a loss?
| Condition | Result | Formula |
|---|
| SP > CP | Profit | Profit = SP - CP |
| CP > SP | Loss | Loss = CP - SP |
| SP = CP | No profit, no loss | -- |
How to Solve a Problem
Step 1: Write down the CP and SP.
Step 2: Compare them -- is SP greater, smaller, or equal to CP?
Step 3: Use the correct formula to find profit or loss.
Examples
Example 1: Finding Profit
A shopkeeper in Ahmedabad buys a school bag for Rs 150 and sells it for Rs 200.
CP = Rs 150, SP = Rs 200. Since SP > CP, there is a profit.
Profit = SP - CP = Rs 200 - Rs 150 = Rs 50.
Example 2: Finding Loss
Sunita buys a water bottle for Rs 120 and sells it for Rs 95.
CP = Rs 120, SP = Rs 95. Since CP > SP, there is a loss.
Loss = CP - SP = Rs 120 - Rs 95 = Rs 25.
Example 3: No Profit, No Loss
A vegetable seller in Bengaluru buys tomatoes for Rs 60 and sells them for Rs 60.
CP = Rs 60, SP = Rs 60. Since SP = CP, there is no profit and no loss.
Example 4: Finding SP When Profit is Given
Gopal buys a cricket bat for Rs 250 and makes a profit of Rs 75. What is the SP?
SP = CP + Profit = Rs 250 + Rs 75 = Rs 325.
Key Words and Meanings
| Word | Meaning |
|---|
| Cost Price (CP) | The price at which a shopkeeper buys an item |
| Selling Price (SP) | The price at which a shopkeeper sells an item |
| Profit | The extra money earned when SP is more than CP |
| Loss | The money lost when SP is less than CP |
⭐ Key Points to Remember
- CP is the buying price. SP is the selling price.
- If SP > CP, there is a profit. Profit = SP - CP.
- If CP > SP, there is a loss. Loss = CP - SP.
- If SP = CP, there is no profit and no loss.
- SP = CP + Profit, or SP = CP - Loss.
- Always write CP and SP clearly before solving.
Practice Questions
A. Fill in the Blanks
1. The price at which a shopkeeper buys an item is called the .
2. The price at which a shopkeeper sells an item is called the .
3. If SP is greater than CP, the shopkeeper makes a .
4. If CP is greater than SP, the shopkeeper suffers a .
5. Profit = - .
B. Multiple Choice Questions
1. A toy is bought for Rs 45 and sold for Rs 60. The profit is:
(a) Rs 10(b) Rs 15(c) Rs 20(d) Rs 105
2. CP = Rs 80, SP = Rs 65. This is a case of:
(a) Profit(b) Loss(c) No profit, no loss(d) Cannot tell
3. If CP = Rs 100 and Profit = Rs 30, then SP is:
(a) Rs 70(b) Rs 100(c) Rs 130(d) Rs 300
C. Find Profit or Loss
| Item | CP (Rs) | SP (Rs) | Profit or Loss? | Amount (Rs) |
|---|
| Pen | 12 | 18 | | |
| Eraser | 8 | 5 | | |
| Ruler | 15 | 20 | | |
| Sharpener | 10 | 10 | | |
| Lunch box | 175 | 200 | | |
D. Solve These Word Problems (Show All Steps)
1. A fruit seller in Mumbai buys oranges for Rs 90 and sells them for Rs 125. Find the profit.
2. Lakshmi buys a saree for Rs 350 and sells it for Rs 310. Find the loss.
3. A shopkeeper buys a clock for Rs 275 and makes a profit of Rs 50. What is the selling price?
Think and Do -- Fun Activity
My Little Shop: Imagine you are a shopkeeper at a school mela. You buy 5 items and sell them. Fill in the table below with your own numbers and find the profit or loss for each item.
| Item | CP (Rs) | SP (Rs) | Profit / Loss | Amount (Rs) |
|---|
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
Total Profit earned: Rs __________ Total Loss suffered: Rs __________