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Profit is a fundamental concept in mathematics and business, representing the financial gain when the selling price of an item is more than its cost price. Understanding profit is crucial not just for competitive exams like SSC and Banking, but also in everyday life, whether you're buying vegetables, selling an old phone, or running a small business. For instance, if you buy a book for Rs. 200 and sell it for Rs. 250, the extra Rs. 50 you earned is your profit.
In competitive exams, questions on Profit and Loss are very common and test your ability to apply basic arithmetic concepts to real-world business scenarios. To master this topic, it's essential to understand the core terms:
Here are the fundamental formulas you need to know:
1. Profit:
Profit = SP - CP (when SP > CP)
2. Loss:
Loss = CP - SP (when CP > SP)
3. Profit Percentage (%):
Profit % = (Profit / CP) × 100
This tells us the profit as a percentage of the cost price. It's crucial to remember that profit percentage is always calculated on the Cost Price unless otherwise specified.
4. Loss Percentage (%):
Loss % = (Loss / CP) × 100
Similar to profit percentage, loss percentage is also calculated on the Cost Price.
Example: If an item is bought for Rs. 500 (CP) and sold for Rs. 600 (SP).
Example: If an item is bought for Rs. 500 (CP) and sold for Rs. 450 (SP).
These formulas are incredibly useful for quickly finding SP or CP when percentages are given:
1. If there is a Profit of P%:
SP = CP × (100 + P) / 100
2. If there is a Loss of L%:
SP = CP × (100 - L) / 100
Conversely, to find CP when SP and percentage are known:
1. If there is a Profit of P%:
CP = SP × 100 / (100 + P)
2. If there is a Loss of L%:
CP = SP × 100 / (100 - L)
Understanding these interrelationships and practicing with various problems will help you solve complex questions quickly and accurately in your exams. Remember that all calculations of profit or loss percentage are always based on the Cost Price unless the question explicitly states otherwise, for example, 'profit on selling price'.
Profit
Profit = SP - CPLoss
Loss = CP - SPProfit Percentage
Profit % = (Profit / CP) × 100Loss Percentage
Loss % = (Loss / CP) × 100Selling Price (with Profit)
SP = CP × (100 + Profit %) / 100Cost Price (with Loss)
CP = SP × 100 / (100 - Loss %)| Aspect | Profit | Loss |
|---|---|---|
| Condition | SP > CP | CP > SP |
| Formula (Absolute) | SP - CP | CP - SP |
| Formula (Percentage) | (Profit/CP) × 100 | (Loss/CP) × 100 |
| Effect on Business | Financial Gain | Financial Setback |
Q: A shopkeeper buys an article for Rs. 400 and sells it for Rs. 520. Find the profit and profit percentage.
Q: By selling an article for Rs. 640, a shopkeeper incurs a loss of 20%. What was the cost price of the article?
Q: A vendor buys 10 lemons for Rs. 15 and sells them at Rs. 2 per lemon. Find his overall profit or loss percentage.
Q: A dealer sells two articles for Rs. 990 each. On one, he gains 10%, and on the other, he loses 10%. Find his overall gain or loss percentage.
You bought a new smart TV during the Diwali sale for Rs. 40,000 after a 20% discount. The shopkeeper had originally marked it up by 25% on his cost price. What was the shopkeeper's original cost price for the TV?
A cricket equipment shop buys a bat for Rs. 5000. They want to make a 15% profit. What should be their selling price?
You sold your old smartphone for Rs. 12,000. You had bought it for Rs. 15,000 three years ago. What was your loss percentage in this deal?
A coffee shop sells a cup of coffee for Rs. 150, making a 50% profit on its cost. If the rent increases, they now want to make a 60% profit. What should be the new selling price of the coffee?
A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 900 grams for 1 kg. What is his profit percentage?
If the selling price of an article is 4/3 times its cost price, what is the profit percentage?
A reduction of 20% in the price of sugar enables a purchaser to obtain 5 kg more for Rs. 100. The original price of sugar per kg was:
A reduction of 20% in the price of sugar enables a purchaser to obtain 5 kg more for Rs. 100. The original price of sugar per kg was:
A person buys an article for Rs. 1200 and sells it at a profit of 25%. If he sells it through an agent who charges a commission of 10% on the selling price, what is his actual profit?
1If an article is bought for Rs. 500 and sold for Rs. 550, what is the profit percentage?
2A shopkeeper sells an item for Rs. 800 at a loss of 20%. What was its cost price?
3By selling 20 articles, a person gains the cost price of 5 articles. Find the profit percentage.
4A man sells an article at a profit of 10%. If he had bought it at 10% less and sold it for Rs. 20 more, he would have gained 40%. What is the cost price of the article?
5A man sells an article at a profit of 10%. If he had bought it at 10% less and sold it for Rs. 20 more, he would have gained 40%. What is the cost price of the article?
6A man sells an article at a profit of 10%. If he had bought it at 10% less and sold it for Rs. 80 more, he would have gained 40%. What is the cost price of the article?
7A man sells an article at a profit of 10%. If he had bought it at 10% less and sold it for Rs. 20 more, he would have gained 40%. What is the cost price of the article?
Profit = SP - CPLoss = CP - SPProfit % = (Profit / CP) × 100+3 more formulas below