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Profit and Loss Formula is used to determine the rate of an item in the market and whether the business is profitable or not. It is always calculated on the cost price.
- Profit and Loss Formula calculates the loss or profit which is incurred by selling a particular product.
- Loss is the amount lost during a purchase or sale, while profit is the amount gained.
- When the price at which a product is sold is more than the price at which the product was bought, profit takes place.
- Loss occurs when the price at which the product is sold is less than the price at which the product is sold.
- Each object or item has a cost price and a selling price.
- On the basis of these values, profit and loss can be calculated for an object.
- When an individual is creating a monthly budget to track the personal expenses of his house.
- This is the real-life example of profit and loss formula.
Key Terms: Profit and Loss Formula, Profit, Loss, Selling Price, Cost Price, Marked Price, Profit Percentage, Loss Percentage, Fixed Cost, Variable Cost, Discount
What is the Profit and Loss Formula?
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Profit and Loss Formula is used to determine whether a transaction is profitable or not. This in turn will determine whether the sale is advantageous or not. The profit and loss formula is discussed in detail in below section:
Profit Formula
Profit is defined as amount gained by seller when a product or service is sold at a selling price more than its cost price. When a transaction ends in profit, the product/service is sold to a customer at a price higher than original price.
- In case of profit, Selling Price (SP) is greater than Cost Price (CP).
- Therefore, Profit Formula is given as,
Profit (P) = Selling Price (SP) - Cost Price (CP)
Example of Profit FormulaExample: Suppose a shopkeeper has bought 1 kg of apples for 100 rs. And sold it for Rs. 120 per kg. How much is the profit gained by him? Solution: Cost Price for apples is 200 rs. Selling Price for apples is 220 rs. Then profit gained by shopkeeper is ; P = SP – CP P = 220 – 200 = Rs. 20/- |
Loss Formula
Loss is defined as amount lost by seller when a product or service is sold at a selling price less than its cost price. When a transaction ends in loss, the product /service is sold to a customer at a price lower than the original price.
- In case of loss, cost price(CP) is greater than the selling price (SP).
- Therefore, the formula for profit is given as,
Loss (L) = Cost Price (CP) - Selling Price (SP)
Example of Loss FormulaExample: Suppose a shopkeeper has bought 1 kg of apples for 200 rs. And sold it for Rs. 120 per kg. How much is the profit gained by him? Solution: Cost Price for apples is 200 rs. Selling Price for apples is 120 rs. Then loss by shopkeeper is ; P = CP – SP L = 200 – 120 = Rs. 80/- |
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| Profit Loss Interest | Ratio to Percentage | Real Number System |
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Profit and Loss Percentage
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The profit and loss percentage is as follows:
Profit Percentage
Profit percentage obtained in a transaction can be calculated using profit percentage formula. The percentage of profit is calculated by dividing profit gained by cost price (CP) of the product involved in the transaction.
- Lastly multiply the result obtained with 100.
Profit Percentage (%) = (Profit (P)/ Cost Price (CP)) x 100
Loss Percentage
Loss percentage that occurred in a transaction can be calculated using loss percentage formula. The percentage of loss is calculated by dividing Loss occurred by cost price (CP) of the service or product involved in the transaction.
- Lastly multiply the result obtained with 100.
Loss Percentage (%) = (Loss (L) /Cost Price (CP)) x 100
Difference Between Profit and Loss Formulas
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Following table provides key differences between Profit and Loss Formula:
| Profit Formula | Loss Formula |
|---|---|
| In case of profit, the selling price (SP) is greater than cost price (CP). | In case of loss, cost price (CP) is greater than the selling price (SP). |
| When the selling price (SP) and cost price (CP) is given, Profit (P) is calculated using the formula, Profit (P) = Selling Price (SP) - Cost Price (CP) | When the selling price (SP) and cost price (CP) is given, Loss (L) is calculated using the formula, Loss (L) = Cost Price (CP) - Selling Price (SP) |
| When Profit (P) and cost price (CP) is given, Profit percentage is calculated using the formula, Profit Percentage (%) = Profit (P) Cost Price (CP) 100 | When Profit (P) and cost price (CP) is given, Profit percentage is calculated using the formula, Loss Percentage (%) = Loss (L) Cost Price (CP) 100 |
| When Profit (P) and cost price (CP) is given, the selling price (SP) is calculated using the formula, Selling Price (SP) = Cost Price (CP) + Profit (P) | When Loss (L) and cost price (CP) is given, the selling price (SP) is calculated using the formula, Selling Price (SP) = Cost Price (CP)- Loss (L) |
| When Profit (P) and selling price (SP) is given, cost price (CP) is calculated using the formula, Cost Price (CP) = Selling Price (SP) - Profit (P) | When Loss (L) and selling price (SP) is given, cost price (CP) is calculated using the formula, Cost Price (CP) = Selling Price (SP) + Loss (L) |
| When Profit percentage and cost price (CP) is given, Profit (P) is calculated using the formula, Profit (P) = Profit Percentage (%) 100 Cost Price (CP) | When Loss percentage and cost price (CP) is given, Loss (L) is calculated using the formula, Loss (L) = Loss Percentage (%) 100 Cost Price (CP) |
Profit and Loss Basic Concepts
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Following are some important terms related to profit and loss:
Selling Price (SP)
Selling price is the price at which a product or service is sold. If a shopkeeper bought 1kg of apple for INR 60 and then sold it to a customer at INR 100, then the selling price (SP) of the apple is INR 100.
Cost Price (CP)
Cost price is the price at which a product or service is purchased. If a shopkeeper bought 1kg of apple for INR 60 and then sold it to a customer at INR 100, then cost price (CP) of the apple is INR 60.
- Cost price is further categorized as the fixed cost and variable cost.
Marked Price (MP)
The marked price is a pre-labeled rate of a product or service done by the shopkeeper or manufacturer to provide a discount offer to their customers.
Discount
A discount is a deduction offered by a seller to the buyer at the marked price. Discount is basically referred to as the marked price (MP) minus the selling price(SP).
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Things to Remember
- Profit and loss formula is to determine the profit or loss for an object.
- Loss is amount lost by the seller when a product or service is sold at a selling price less than its cost price.
- Profit is amount gained by seller when a product or service is sold at a selling price more than its cost price.
- When profit (P) and cost price (CP) are given, profit percentage is calculated using the formula, Profit Percentage (%) = Profit(P)/Cost Price (CP)x100
- Cost price (CP) is calculated using the formula, Cost Price (CP) =Selling Price (SP) - Profit (P), when Profit (P) and the selling price (SP) are given.
Sample Questions
Ques. Which concept is applicable for calculation of profit loss? (2 Marks)
Ans. Amount of profit or loss incurred is based on the Cost price. The formulas that are used to calculate the profit and loss percentage are given below: Profit percentage (P%) = (Profit /Cost Price) × 100. Loss percentage (L%) = (Loss / Cost price) × 100.
Ques. The original price of a book is INR 50 and it is sold by a shopkeeper at INR 80. Calculate profit earned by the shopkeeper. (4 Marks)
Ans. The original /actual price of the book = INR 50
cost price (CP) of the book = INR 50
Also, the book is sold to a customer by the shopkeeper at a price of INR 80
selling price (SP) of the book = INR 80
Profit is calculated using the formula, Profit (P)= Selling Price (SP) - Cost Price (CP), when the selling price (SP) and cost price (CP) are given.
So, Profit (P)= 80 - 50
Profit (P) =30
Therefore, profit earned by the shopkeeper is INR 30.
Ques. A shopkeeper bought 1 kg of oranges at a price of INR 50 and sold it to a customer for a profit of 5 %. Find the price at which the shopkeeper sold the 1 kg oranges to the customer. (4 Marks)
Ans. The shopkeeper bought 1 kg of oranges at a price of INR 50.
Cost Price (CP) of the oranges = INR 50
Profit percentage = 5%
Profit percentage is calculated using the formula,
Profit Percentage (%) = Profit (P) Cost Price (CP)100, when Profit and cost price are given.
So, when Profit percentage and cost price (CP) are given, profit is calculated using the formula,
Profit (P)= Profit Percentage (%)100Cost Price (CP)
So, Profit (P)= 510050
Therefore, Profit gained by the shopkeeper = INR 2.5
Ques. Original price of a shirt is INR 200 and it is sold by a shopkeeper at INR 350. Calculate Profit earned by the shopkeeper. (4 Marks)
Ans. Original /actual price of shirt = INR 200
Cost price (CP) of shirt = INR 200
Also, the shirt is sold to a customer by the shopkeeper at a price of INR 350
Selling Price (SP) of the shirt = INR 350
Profit is calculated using the formula, Profit (P)= Selling Price (SP) - Cost Price (CP), when the selling price (SP) and cost price (CP) are given.
So, Profit (P)= 350- 200
Profit (P) =150
Therefore, Profit earned by the shopkeeper is INR 150.
Ques. A child bought chocolates from the shopkeeper at a price of INR 30 and then sold the chocolate to his friend for INR 25. Calculate Loss that the child had. (4 Marks)
Ans. Child bought chocolates from the shopkeeper at a price of INR 30.
Cost price (CP) of the chocolate = INR 30
Chocolates were sold to his friend for INR 25.
Selling price (SP) of the chocolate = INR 25
Loss (L) is calculated using the formula,
Loss (L)= Cost Price (CP) - Selling Price (SP), when the selling price (SP) and cost price (CP) are given.
So, Loss (L)= 30 - 25
Loss (L) =5
Therefore, Loss the child had is INR 5.
Ques. Manu bought five books at a cost of INR 100 and sold them to his friend at a profit of INR 50. Find the price at which Manu sold the five books to his friend. (4 Marks)
Ans. Given that Manu bought five books at a cost of INR 100.
Cost price (CP) of the five books = INR 100
Also, Profit earned by Manu = INR 50
Profit (P) = INR 50
Formula to calculate the selling price of a product /service is given as,
Selling Price (SP) = Cost Price (CP) + Profit (P), when cost price (CP) and Profit (P) are given.
So, Selling Price (SP) = 100+ 50
Selling Price(SP)=150
Therefore, the price at which Manu sold the five books he bought to his friend at profit is INR 150.
Ques. Calculate Loss percentage when a shopkeeper had a loss of INR 200 and his product was sold at a price of INR 100. (4 Marks)
Ans. Product was sold by the shopkeeper at a price of INR 100.
Selling price (SP) = INR 100
Also, given that Loss = INR 200
Cost price (CP) in this case is calculated using the formula,
Cost Price (CP) =Selling Price (SP) + Loss (L)
So, Cost Price (CP) = 100 +200
Cost Price (CP) = 300
Now, formula for calculating Loss percentage when Loss (L) and cost price (CP) are given is,
Loss Percentage (%) = Loss(L)Cost Price (CP)100
So, Loss Percentage (%) = 200300100
Loss Percentage (%) =66.67%
Therefore, Loss percentage is 66.67%.
Ques. Actual price of a pair of pens is INR 20 and it is sold by a shopkeeper at INR 10. Find whether the shopkeeper had a profit or loss and by what margin. (5 Marks)
Ans. Original/actual price of the pair of pens = INR 20
Cost price (CP) of the pair of pens = INR 20
Also, the pair of pens are sold to a customer by the shopkeeper at a price of INR 10
Selling price (SP) of the pair of pens = INR 10
In the given question, cost price (CP) is greater than the selling price (SP).
Hence, the shopkeeper had a loss in the business.
Now, Loss (L) is calculated using the formula,
Loss (L)= Cost Price (CP) - Selling Price (SP), when the selling price (SP) and cost price (CP) are given.
So, Loss (L)= 20 - 10
Loss (L) =10
Therefore, Loss the shopkeeper had is INR 10.
Ques. The original price of a book is INR 80 and it is sold by a shopkeeper at INR 120. Calculate profit earned by the shopkeeper. (4 Marks)
Ans. The original /actual price of the book = INR 80
cost price (CP) of the book = INR 80
Also, the book is sold to a customer by the shopkeeper at a price of INR 120
selling price (SP) of the book = INR 120
Profit is calculated using the formula, Profit (P)= Selling Price (SP) - Cost Price (CP), when the selling price (SP) and cost price (CP) are given.
So, Profit (P)= 120 - 80
Profit (P) =40
Therefore, profit earned by the shopkeeper is INR 40.
Ques. A shopkeeper bought 1 kg of oranges at a price of INR 100 and sold it to a customer for a profit of 5 %. Find the price at which the shopkeeper sold the 1 kg oranges to the customer. (4 Marks)
Ans. The shopkeeper bought 1 kg of oranges at a price of INR 100.
Cost Price (CP) of the oranges = INR 100
Profit percentage = 5%
Profit percentage is calculated using the formula,
Profit Percentage (%) = Profit (P) Cost Price (CP)100, when Profit and cost price are given.
So, when Profit percentage and cost price (CP) are given, profit is calculated using the formula,
Profit (P)= Profit Percentage (%)100Cost Price (CP)
So, Profit (P)= 5 x 100/100
Therefore, Profit gained by the shopkeeper = INR 5
Ques. Original price of a shirt is INR 100 and it is sold by a shopkeeper at INR 350. Calculate Profit earned by the shopkeeper. (4 Marks)
Ans. Original /actual price of shirt = INR 100
Cost price (CP) of shirt = INR 100
Also, the shirt is sold to a customer by the shopkeeper at a price of INR 350
Selling Price (SP) of the shirt = INR 350
Profit is calculated using the formula, Profit (P)= Selling Price (SP) - Cost Price (CP), when the selling price (SP) and cost price (CP) are given.
So, Profit (P)= 350- 100
Profit (P) =250
Therefore, Profit earned by the shopkeeper is INR 250.
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