Profit and Loss Formula

Profits are a financial gain, in particular the difference between the amount earned and the amount spent on the purchase, operation or production.

A loss occurs when a product is sold at a lower cost. Loss is often reflected in the cost price percentage.

The profit and loss formula is a mathematical formula that is used to calculate the selling price of a product and to determine how profitable a company is. There is a cost price and a selling price for any product. We may measure the profit or loss made for a specific product based on the values of these prices.

Example: If a student buys a bicycle for Rs. 10000 and sells it for Rs. 12000 to his friend then the student is having a profit of Rs. 2000. Now if the same student sells the bicycle for Rs. 8000, then the student is having a loss of Rs. 2000. 

Now let us understand the basic concepts involved in the formula of profit and loss. Here we will discuss all formula of profit and loss in detail with numerical examples.

Profit and Loss Math Basic Concepts

Cost Price

The cost price is the price at which a merchant or retailer buys or has bought goods. Actual cost, last cost, average cost, and net realisable value are all forms of cost prices.

Selling Price

The selling price is the price at which a shopkeeper sells a product or service to a consumer.

CP SP Formula

Cost price formula when profit percentage and selling price are given:

CP = \[\frac{(SP \times 100)}{(100 + Profit \%)}\]

Cost price formula when loss percentage and selling price are given:

CP = \[\frac{(SP \times 100)}{(100 - loss \%)}\]

Selling price formula when profit percentage and cost price are given:

SP = \[\frac{(100 + Profit \%)}{100}\] x CP

Selling price formula when loss percentage and cost price are given:

SP = \[\frac{(100 - loss \%)}{100}\] x CP

Marked Price

The marked price or list price is the price on the label of an article or product. This is the price at which the product will be offered for sale. However, there may be a discount applied to this price, and the product's actual sale price may be lower than the marked price. 

A discount is a refund or a deal made by a shopkeeper to entice consumers to buy something.

Marked price is given by the formula: 

Marked price = Discount + Selling price

The percentage discount formula in profit and loss is given by the formula:

Percentage Discount = (Discount / Marked price) × 100

Profit

When the selling price is more than the cost price, then the person will obtain profit.

Profit = SP > CP.

Loss

When the selling price is less than the cost price, then the person will obtain loss.

Loss = SP < CP.

Formula of Profit and Loss

The profit loss formula is given as follows:

Profit or Gain = Selling price - Cost price

Loss = Cost price - Selling price

Profit and Loss Percentage Formula

In order to calculate profit and loss, the concepts of fraction and percentage are used. In certain cases, profit or loss is calculated as a percentage of the cost price. Find the profit or loss using the profit formula, then convert it to a profit or loss percentage by expressing it as a fraction with the cost price as the denominator.

The formula of profit percentage is given as follows:

Profit Percentage = \[\frac{Profit}{\text{Cost Price}}\] x 100

The formula of loss percentage is given as follows:

Loss Percentage = \[\frac{Loss}{\text{Cost Price}}\] x 100

Problems on Profit and Loss Formula

1) A student purchases a book for Rs. 35. If the marked price on the book is Rs. 40. What will be the discount given to the student? Also, calculate the percentage discount.

Ans: Here the marked price of the book is Rs. 40 and the selling price of the book is Rs. 35. So by using the discount formula, we will get the discount the student obtained after purchasing the book.

Discount = Marked price - Selling price

Substituting the values,

Discount = 40 - 35

Discount = Rs. 5

So the student obtains a discount of Rs. 5. 

Now to calculate the percentage discount we will use the formula as follows:

Percentage Discount = (Discount / Marked price) × 100

Now substituting the values we get

Percentage Discount = (5 / 40) × 100

Percentage Discount = (0.125) × 100

Percentage Discount = 12.5 %

So the percentage discount obtained by the student after purchasing the book is 12.5%.

2) The shopkeeper purchases the book for Rs. 100 and he sells it to the student for Rs.125. By using the profit formula math calculate the profit obtained by the shopkeeper and also find the profit percentage.

Ans: Here the cost price of the book is CP = Rs. 100.

The selling price of the book is SP = Rs.125.

So the profit will be the difference between the selling price and cost price.

Profit or Gain = Selling price - Cost price

Profit = 125 - 100

Profit = Rs. 25.

So by selling the book to the student the shopkeeper obtains a profit of Rs. 25.

Now to calculate the profit percentage the formula of profit percentage is as follows:

Profit Percentage = \[\frac{Profit}{\text{Cost Price}}\] x 100

Substituting the values we get the profit percentage as 

Profit percentage = (25 / 100) × 100

Profit percentage = (0.25) × 100

Profit percentage = 25%

So the percentage profit obtained by the shopkeeper is 25%.

3) The shopkeeper purchases the pen for Rs. 80 and he sells it to the student for Rs.70. By using the loss formula calculate the loss obtained by the shopkeeper and also find the loss percentage.

Ans: Here the cost price of the pen is CP = Rs. 80.

The selling price of the pen is SP = Rs.70.

So the loss will be the difference between the cost price and the selling price.

Loss = Cost price - Selling price

Loss = 80 - 70

Loss = Rs. 10.

So by selling the pen to the student the shopkeeper ends up with a loss of Rs. 10.

Now to calculate the loss percentage the formula is as follows:

Loss Percentage = \[\frac{Loss}{\text{Cost Price}}\] x 100

Substituting the values we get the loss percentage as, 

Loss percentage = (10 / 80) × 100

Loss percentage = (0.125) × 100

Loss percentage = 12.5%

So the percentage loss obtained by the shopkeeper is 12.5%.

4) If a student purchases a book for Rs. 180 with a 20% discount. Calculate the cost price of the book.

Ans: Here the selling price of the book is SP = Rs. 180.

Discount = 20%

Here the student is getting a discount on the book so it means that the shopkeeper is selling the book less than the cost price and he is at loss. So to find the cost price of the book use the selling price formula

SP = \[\frac{(100 - loss %)}{100}\] x CP

Substituting the values

180 = \[\frac{(100 - 20)}{100}\] x CP

180 = \[\frac{(80)}{100}\] x CP

180 = 0.8 x CP

CP =  \[\frac{180}{0.8}\]

CP = Rs. 225

Therefore the cost price of the book is Rs. 225.

5) A student buys 10 notebooks for Rs. 500 and sells them at a 10% loss. Calculate the cost price of 10 notebooks.

Ans: Here the selling price of 10 notebooks is SP = Rs. 500.

Loss percentage = 10%

Here the student is selling the notebooks at a 10% loss. So to find the cost price of 10 notebooks we have to use the selling price formula as follows:

SP = \[\frac{(100 - loss %)}{100}\] x CP

Now substituting the values we get,

500 = \[\frac{(100 - 10)}{100}\] x CP

500 = \[\frac{(90)}{100}\] x CP

500 = 0.9 x CP

CP = \[\frac{(500)}{0.9}\] 

CP = Rs. 555

Therefore the cost price of 10 notebooks is Rs.555 and the student has a loss of Rs. 55 after selling 10 notebooks.

Conclusion

A profit and loss account is one of a company's financial statements that reflects the company's sales and expenditures over time. After all revenues and expenditures have been accounted for, it shows how the revenues are converted into net income or net profit. The income statement's aim is to show managers and investors whether the business made money (profit) or lost money (loss) during the time span under consideration.