Profit and Loss
Think about a shopkeeper who buys a toy for Rs. 80 and sells it for Rs. 100. He made Rs. 20 extra. That extra money is called profit. Now imagine another shopkeeper who buys a bag for Rs. 500 but can only sell it for Rs. 450. He lost Rs. 50. That loss of money is called loss.
Every business, from a small street vendor selling fruits to a large company making cars, works on this idea. They buy things at one price and sell at another. If the selling price is more than what they paid, they earn a profit. If the selling price is less, they suffer a loss.
But just knowing the profit or loss in rupees is not always enough. Suppose one person makes Rs. 50 profit on an item that cost Rs. 100, and another person makes Rs. 50 profit on an item that cost Rs. 500. Who did better? The first person! Because Rs. 50 on Rs. 100 is 50% profit, while Rs. 50 on Rs. 500 is only 10% profit. This is why we calculate profit percentage and loss percentage.
In this chapter, you will learn the meaning of cost price, selling price, profit, loss, and how to calculate profit% and loss% using simple formulas. We will use everyday examples like buying and selling books, fruits, and school supplies.
What is Profit and Loss?
Key Terms:
| Term | Meaning | Example |
|---|---|---|
| Cost Price (C.P.) | The price at which an item is bought | A pen bought for Rs. 10 has C.P. = Rs. 10 |
| Selling Price (S.P.) | The price at which an item is sold | The pen sold for Rs. 15 has S.P. = Rs. 15 |
| Profit (Gain) | Extra money earned when S.P. > C.P. | Profit = 15 - 10 = Rs. 5 |
| Loss | Money lost when S.P. < C.P. | If pen sold for Rs. 8, Loss = 10 - 8 = Rs. 2 |
| Profit % | Profit expressed as a percentage of C.P. | (5/10) x 100 = 50% |
| Loss % | Loss expressed as a percentage of C.P. | (2/10) x 100 = 20% |
Important:
- Profit and Loss are always calculated on the Cost Price (C.P.).
- If S.P. = C.P., there is no profit and no loss.
- If S.P. > C.P., there is a profit.
- If S.P. < C.P., there is a loss.
Profit and Loss Formula
Profit and Loss Formulas:
Profit = Selling Price (S.P.) - Cost Price (C.P.)
(when S.P. > C.P.)
Loss = Cost Price (C.P.) - Selling Price (S.P.)
(when C.P. > S.P.)
Percentage Formulas:
Profit % = (Profit / C.P.) x 100
Loss % = (Loss / C.P.) x 100
Finding S.P. when Profit% is given:
S.P. = C.P. + (Profit% / 100) x C.P.
Or: S.P. = C.P. x (100 + Profit%) / 100
Finding S.P. when Loss% is given:
S.P. = C.P. - (Loss% / 100) x C.P.
Or: S.P. = C.P. x (100 - Loss%) / 100
Types and Properties
Profit and loss problems can be grouped into several types:
Type 1: Finding Profit or Loss Amount
Given C.P. and S.P., find the profit or loss. Simply subtract: Profit = S.P. - C.P. (if S.P. > C.P.) or Loss = C.P. - S.P. (if C.P. > S.P.).
Type 2: Finding Profit% or Loss%
Given C.P. and S.P., find profit or loss first, then use: Profit% = (Profit/C.P.) x 100 or Loss% = (Loss/C.P.) x 100.
Type 3: Finding S.P. when C.P. and Profit% are Given
Use: S.P. = C.P. x (100 + Profit%)/100.
Type 4: Finding S.P. when C.P. and Loss% are Given
Use: S.P. = C.P. x (100 - Loss%)/100.
Type 5: Finding C.P. when S.P. and Profit% are Given
Use: C.P. = S.P. x 100 / (100 + Profit%).
Type 6: Finding C.P. when S.P. and Loss% are Given
Use: C.P. = S.P. x 100 / (100 - Loss%).
Type 7: Word Problems
Real-life problems about buying and selling. Read carefully, identify C.P. and S.P., then apply the correct formula.
Quick Summary Table:
| Given | Find | Formula |
|---|---|---|
| C.P., S.P. | Profit or Loss | S.P. - C.P. or C.P. - S.P. |
| C.P., S.P. | Profit% or Loss% | (Profit or Loss / C.P.) x 100 |
| C.P., Profit% | S.P. | C.P. x (100 + Profit%) / 100 |
| C.P., Loss% | S.P. | C.P. x (100 - Loss%) / 100 |
| S.P., Profit% | C.P. | S.P. x 100 / (100 + Profit%) |
| S.P., Loss% | C.P. | S.P. x 100 / (100 - Loss%) |
Solved Examples
Example 1: Finding Profit and Profit%
Problem: A shopkeeper buys a calculator for Rs. 250 and sells it for Rs. 300. Find the profit and profit%.
Solution:
Given:
- C.P. = Rs. 250
- S.P. = Rs. 300
Since S.P. > C.P., there is a profit.
- Profit = S.P. - C.P. = 300 - 250 = Rs. 50
- Profit% = (Profit / C.P.) x 100
- = (50 / 250) x 100
- = (1/5) x 100
- = 20%
Answer: Profit = Rs. 50, Profit% = 20%
Example 2: Finding Loss and Loss%
Problem: Suresh buys a bicycle for Rs. 3500 and sells it for Rs. 3150. Find the loss and loss%.
Solution:
Given:
- C.P. = Rs. 3500
- S.P. = Rs. 3150
Since C.P. > S.P., there is a loss.
- Loss = C.P. - S.P. = 3500 - 3150 = Rs. 350
- Loss% = (Loss / C.P.) x 100
- = (350 / 3500) x 100
- = (1/10) x 100
- = 10%
Answer: Loss = Rs. 350, Loss% = 10%
Example 3: Finding S.P. from C.P. and Profit%
Problem: A book is bought for Rs. 180. The shopkeeper wants to make 25% profit. What should be the selling price?
Solution:
Given:
- C.P. = Rs. 180
- Profit% = 25%
Using the formula:
- Profit = (25/100) x 180 = Rs. 45
- S.P. = C.P. + Profit = 180 + 45 = Rs. 225
Answer: The selling price should be Rs. 225.
Example 4: Finding S.P. from C.P. and Loss%
Problem: A mobile phone is bought for Rs. 8000. It is sold at a loss of 15%. Find the selling price.
Solution:
Given:
- C.P. = Rs. 8000
- Loss% = 15%
Using the formula:
- Loss = (15/100) x 8000 = Rs. 1200
- S.P. = C.P. - Loss = 8000 - 1200 = Rs. 6800
Answer: The selling price is Rs. 6800.
Example 5: Finding C.P. from S.P. and Profit%
Problem: A chair is sold for Rs. 1320 at a profit of 10%. Find the cost price.
Solution:
Given:
- S.P. = Rs. 1320
- Profit% = 10%
Using the formula:
- C.P. = S.P. x 100 / (100 + Profit%)
- = 1320 x 100 / (100 + 10)
- = 132000 / 110
- = Rs. 1200
Verification: Profit = 10% of 1200 = Rs. 120. S.P. = 1200 + 120 = Rs. 1320. Correct!
Answer: The cost price is Rs. 1200.
Example 6: Fruit Seller Word Problem
Problem: A fruit seller buys 200 oranges for Rs. 1000. He sells them at Rs. 6 each. Find his profit or loss and the profit% or loss%.
Solution:
Given:
- C.P. of 200 oranges = Rs. 1000
- S.P. of 1 orange = Rs. 6
- S.P. of 200 oranges = 200 x 6 = Rs. 1200
Since S.P. > C.P., there is a profit.
- Profit = 1200 - 1000 = Rs. 200
- Profit% = (200/1000) x 100 = 20%
Answer: Profit = Rs. 200, Profit% = 20%
Example 7: Two Items - Overall Profit or Loss
Problem: Anita bought two sarees. She bought the first for Rs. 1200 and sold it for Rs. 1350. She bought the second for Rs. 1800 and sold it for Rs. 1710. Find the overall profit or loss.
Solution:
Saree 1:
- C.P. = Rs. 1200, S.P. = Rs. 1350
- Profit = 1350 - 1200 = Rs. 150
Saree 2:
- C.P. = Rs. 1800, S.P. = Rs. 1710
- Loss = 1800 - 1710 = Rs. 90
Overall:
- Total C.P. = 1200 + 1800 = Rs. 3000
- Total S.P. = 1350 + 1710 = Rs. 3060
- Overall Profit = 3060 - 3000 = Rs. 60
- Overall Profit% = (60/3000) x 100 = 2%
Answer: Overall profit = Rs. 60, Overall profit% = 2%
Example 8: No Profit No Loss
Problem: A table is bought for Rs. 2500 and sold for Rs. 2500. What is the profit or loss?
Solution:
Given:
- C.P. = Rs. 2500
- S.P. = Rs. 2500
Since C.P. = S.P.:
- There is no profit and no loss.
- Profit = 0, Loss = 0
- Profit% = 0%, Loss% = 0%
Answer: No profit, no loss.
Example 9: Stationery Shop Problem
Problem: A shopkeeper buys 10 pens for Rs. 50 each and sells all of them for a total of Rs. 600. Find the profit% or loss%.
Solution:
Given:
- C.P. of 10 pens = 10 x 50 = Rs. 500
- S.P. of 10 pens = Rs. 600
Since S.P. > C.P.:
- Profit = 600 - 500 = Rs. 100
- Profit% = (100/500) x 100 = 20%
Answer: Profit% = 20%
Example 10: Finding C.P. from S.P. and Loss%
Problem: A watch is sold for Rs. 1360 at a loss of 15%. Find the cost price.
Solution:
Given:
- S.P. = Rs. 1360
- Loss% = 15%
Using the formula:
- C.P. = S.P. x 100 / (100 - Loss%)
- = 1360 x 100 / (100 - 15)
- = 136000 / 85
- = Rs. 1600
Verification: Loss = 15% of 1600 = Rs. 240. S.P. = 1600 - 240 = Rs. 1360. Correct!
Answer: The cost price is Rs. 1600.
Real-World Applications
Profit and loss concepts are used in many real-life situations:
Shopkeeping: Every shopkeeper needs to calculate how much profit they make on each product to run a successful business.
Online Selling: When you sell something on OLX or Quikr, you compare your buying price with the selling price to know if you made a profit or took a loss.
Stock Market: Investors buy shares at one price and sell at another. The difference tells them the profit or loss.
Real Estate: People buy houses or land and sell them later. The difference between buying and selling price determines profit or loss.
Farming: Farmers calculate the cost of seeds, fertiliser, and labour (cost price) and compare it with the price they get for their crops (selling price).
School Fairs: When your school has a fun fair and you set up a stall selling lemonade or crafts, you need to figure out your cost of materials and how much to charge to make a profit.
Key Points to Remember
- Cost Price (C.P.) is the price at which an item is bought.
- Selling Price (S.P.) is the price at which an item is sold.
- If S.P. > C.P., there is a profit. Profit = S.P. - C.P.
- If C.P. > S.P., there is a loss. Loss = C.P. - S.P.
- If C.P. = S.P., there is no profit, no loss.
- Profit% = (Profit / C.P.) x 100. Always calculated on C.P.
- Loss% = (Loss / C.P.) x 100. Always calculated on C.P.
- To find S.P. when profit% is given: S.P. = C.P. x (100 + Profit%) / 100.
- To find S.P. when loss% is given: S.P. = C.P. x (100 - Loss%) / 100.
- Profit% and Loss% help compare deals with different cost prices.
Practice Problems
- A toy is bought for Rs. 120 and sold for Rs. 150. Find the profit and profit%.
- A shirt is bought for Rs. 600 and sold for Rs. 510. Find the loss and loss%.
- A shopkeeper buys a bag for Rs. 400 and wants to make 30% profit. What should be the selling price?
- A laptop is sold for Rs. 36,000 at a loss of 10%. Find the cost price.
- Ram buys 50 notebooks for Rs. 25 each and sells them at Rs. 30 each. Find total profit and profit%.
- A man buys two watches for Rs. 500 each. He sells one at 10% profit and the other at 10% loss. Find the overall profit or loss.
- The cost price of 15 articles is equal to the selling price of 12 articles. Find the profit%.
- A fruit seller buys mangoes at Rs. 40 per dozen and sells them at Rs. 5 each. Find his profit%.
Frequently Asked Questions
Q1. What is profit?
Profit is the extra money earned when the selling price is more than the cost price. Profit = S.P. - C.P. For example, if you buy a pen for Rs. 10 and sell it for Rs. 15, your profit is Rs. 5.
Q2. What is loss?
Loss is the money lost when the selling price is less than the cost price. Loss = C.P. - S.P. For example, if you buy a book for Rs. 200 and sell it for Rs. 170, your loss is Rs. 30.
Q3. Why is profit% calculated on cost price and not selling price?
Profit% is calculated on cost price because C.P. is the amount the seller invested. The percentage tells us how much profit was made relative to the investment. This gives a fair measure of how well the business did.
Q4. What happens when C.P. equals S.P.?
When cost price equals selling price, there is no profit and no loss. The seller breaks even.
Q5. Can profit percentage be more than 100%?
Yes. If an item is bought for Rs. 50 and sold for Rs. 150, profit = Rs. 100, and profit% = (100/50) x 100 = 200%. This means the profit is twice the cost price.
Q6. What is the difference between profit and profit%?
Profit is the actual amount of money gained (in rupees). Profit% is the percentage of profit relative to the cost price. For example, Rs. 50 profit on Rs. 200 C.P. gives profit% = 25%.
Q7. If I sell two items at the same price, one at 10% profit and the other at 10% loss, do I break even?
No, there is always an overall loss in this case. The reason is that the C.P. of the item sold at profit is less, and the C.P. of the item sold at loss is more. The loss amount is greater than the profit amount.
Q8. What is the formula to find C.P. when S.P. and profit% are known?
C.P. = S.P. x 100 / (100 + Profit%). For example, if S.P. = Rs. 660 and profit% = 10%, then C.P. = 660 x 100 / 110 = Rs. 600.
Related Topics
- Introduction to Percentage
- Discount Calculation
- Simple Interest
- Percentage Increase and Decrease
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Word Problems on Profit and Loss
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
