Profit is defined in mathematics as the amount gained from any business goal. When a seller sells a product, he expects to receive some monetary value from the buyer. When we sell a product for more than its cost price, we make a profit. However, if we sell it for less than its cost, we lose money. Any financial benefit gained in a business is known as profit.

The Profit Formula is used to determine the profit earned from the sale of a specific product in a business or the gain in any financial transaction. When the selling price exceeds the cost price, profit can be determined. When businesses do larger transactions, terms like gross profit and net profit are used. Total sales, revenue, a company’s overall profit percentage over time, and so on are examples of these terms.

Let us learn in detail from this article about the profit and profit percentage with the help of formulas and related topics.

Profit

Before we know about profit, let us discuss some terms related to profit. Profit depends on two things, the cost price of a product and the selling price of a product.

Cost Price: The cost at which a product is made is known as cost price. The short form of cost price is \(CP.\)

Selling Price: The price at which we sell a product to the buyer is called the selling price. The short form of the selling price is \(SP.\)

Definition of Profit: If the selling price is more than the cost price in a transaction, then the difference between the selling price and the cost price is profit.

Profits are usually described as profit percentages to define how much profit a business or an individual has made. When \(SP > CP,\) then

\({\rm{Profit}} = SP – CP\)

Learn All the Concepts on Profit and Loss

Let us consider an example. Suppose Rima bought a book at \(₹300\) and sold it at \(₹350.\) Is the transaction profitable? If yes, what is the profit?
Solution: Given that Rima bought the book for \(₹300\)
Hence, \(CP=₹300\)
And she sold the book \(₹350.\)
So, \(SP=₹350\)
We can see here that \(SP > CP.\)
Therefore, the transaction is in profit.
Hence, the profit \( =₹ 350 – ₹300 = ₹50\)
When the selling price is less than the cost price, the difference between the cost and the selling price is considered as loss.
If \(CP > SP,\) then, \({\rm{Loss}} = CP – SP.\)

Types of Profit

There are three kinds of profit used for business purposes. These are:
1. Gross Profit
2. Operating Profit
3. Net Profit

Gross Profit

Gross profit is the profit earned by any company or any individual after removing the cost associated with selling and marketing the product from the selling price. The returns produced in the company’s income after selling the commodity should be reduced by the amount it took to manufacture the product and the packing and distribution expenses before it reaches the customer.

Gross profit evaluates a company’s ability to gain profit while at the same time handling its production and labour costs.

The formula to calculate the gross profit is:
\({\rm{Gross}}\,{\rm{profit}} = {\rm{Revenue}} – {\rm{The}}\,{\rm{cost}}\,{\rm{of}}\,{\rm{goods}}\,{\rm{sold}}\)

Operating Profit

A business’s operating profit says what the role of the company’s operations to its profitability is. The operating profit is the ratio of operating income and sales revenue.

The formula to calculate the operating profit is,
\({\rm{Operating}}\,{\rm{profit}} = {\rm{Gross}}\,{\rm{profit}} – {\rm{Operating}}\,{\rm{expenses}}\)

Net Profit

Net profit is a complete metric for profitability and provides an understanding of how properly the management team operates all the aspects of the business.
It signifies the actual sum of money made by any company.

The formula to calculate the net profit is:
\({\rm{Net}}\,{\rm{profit}} = {\rm{Operating}}\,{\rm{profit}} – \left( {{\rm{Taxes}}\,{\rm{and}}\,{\rm{interest}}} \right)\)

Companies analyse these three types of profit with the help of a profit margin. In such cases, the profit, whether operating, gross, or net, is separated by the return. It shows how well the business uses its profits.

Profit Percentage Formula

We calculate the profit percentage using the following formula:
\({\rm{Profit}}\,\% = \frac{{{\rm{Profit}}}}{{{\rm{Cost}}\,{\rm{Price}}}} \times 100\)

Steps to Calculate the Profit

To calculate the profit earned by any business or any individual, we follow the steps given below:
1. Identify the cost price of the sold products.
2. Determine the total selling price of the sold products.
3. Subtract the cost price from the selling price to identify the profit amount.
4. To determine the profit margin, divide the profit amount with the cost price.

Multiply the profit margin by \(100\) to find the profit percentage.

Some important formulas related to profit are:
1. Profit percentage \(\left( {{\rm{P}}\% } \right) = \left( {\frac{{{\rm{Profit}}}}{{{\rm{Cost}}\,{\rm{Price}}}}} \right) \times 100\% \)
2. Selling price \( = \left\{ {\left( {\frac{{100 + {\rm{P}}\% }}{{100}}} \right)} \right\} \times CP\) (when \(SP > CP\))
3. Cost price \(= \left\{ {\left( {\frac{{100}}{{100 + {\rm{P}}\% }}} \right)} \right\} \times SP\) (when \(SP > CP\))

Use of Profit Calculation

Profit calculations are used in mathematics to know the commodity price and understand how profitable a business is. Every single product has a cost price and a selling price. According to the values of those prices, we can determine the profit earned or the loss acquired for a specific product.

Solved Examples

Q.1. Anamika bought two air coolers at \(₹15000\) each. She sold one at a profit of \(15\% \) and the other at a loss of \(15\% .\) Find whether she made an overall profit or loss.
Ans: Total cost price \( =₹ 15000 + ₹15000 = ₹30000\)
Profit on air cooler machine \(15\%\) of \(₹15000 = \frac{{15}}{{100}} \times ₹15000 = ₹2250\)
\(SP\) of one cooler machine \( = CP + {\rm{Profit}} =₹ \left( {15000 + 2250} \right) = ₹17250\)
Loss on the other cooler machine \(15\%\) of \(₹15000 = \frac{{15}}{{100}} \times ₹15000 = ₹2250\)
\(SP\) of the other cooler machine \( = CP – {\rm{Loss}} = ₹\left( {15000 – 2250} \right) = ₹12750\)
Total \(SP = ₹\left( {17250 + 12750} \right) = ₹30000\)
So, \({\rm{Total}}\,CP = {\rm{Total}}\,SP\)
Hence, neither she made a profit nor a loss.

Q.2. A retailer bought eggs at \(₹42\) per dozen and sells \(5\) eggs for \(₹20.\) Find his gain or loss per cent.
Ans: \(CP\) of \(12\) eggs \( =₹ 42\). Therefore, \(CP\) of \(1\) egg \( =₹ \frac{{42}}{{12}} = ₹\frac{7}{2} = ₹3.50\)
Therefore, \(SP\) of \(5\) eggs \( =₹ 20\) and \(SP\) of \(1\) egg \(₹\frac{{20}}{5} = ₹4\)
Profit on the sale of \(1\) egg \( = ₹\left( {4 – 3.50} \right) = ₹0.50\)
Therefore, profit percentage \( = \frac{{{\rm{Profit}}}}{{{\rm{CP}}}} \times 100\% = \frac{{0.50}}{{3.50}} \times 100\% = \frac{{100}}{7}\% = 14\frac{2}{7}\% \)
Hence, his profit percentage is \(14\frac{2}{7}\% .\)

Q.3. By selling a washing machine for \(₹18858,\) a shopkeeper incurs a profit of \(₹3592.\) Find his profit per cent.
Ans: \(SP\) of TV \(= ₹18858\) and profit \(=₹3592\)
Therefore, \(CP = SP – {\rm{Profit}} = ₹\left( {18858 – 3592} \right) = ₹15266\)
Thus, \({\rm{Profit}}\,\% = \frac{{{\rm{Profit}} \times 100}}{{CP}}\)
\( = \frac{{3592 \times 100}}{{15266}} = 23.52\% \) (approx.)
Hence, his profit per cent is \(23.52\% \) (approx.)

Q.4. A fruit vendor bought \(5\) lemons for \(₹5\) and sold at the rate of \(4\) lemons for \(₹5.\) Calculate:
(a) Profit in selling \(60\) lemons
(b) Profit \(\% \)
Ans:
(a) \(CP\) of \(5\) lemons \( = ₹5\)
\(CP\) of \(1\) lemon \( = \frac{5}{5} = ₹1\)
\(CP\) of \(60\) lemons =1×60=₹60 \(SP\) of \(4\) lemons \( = ₹5\)
\(SP\) of \(1\) lemon \( = \frac{5}{4}\)
\(SP\) of \(60\) lemons \( = \frac{5}{4} \times 60 = ₹75\)
Profit \( = ₹75 – ₹60 = ₹15\)
Hence, the profit is \( = ₹15.\)
(b) \({\rm{Profit}}\,\% = \frac{{{\rm{Profit}}}}{{{\rm{CP}}}} \times 100\)
\( = \frac{{15}}{{60}} \times 100 = 25\% \)
Hence, the profit percentage is \(25\% .\)

Q.5. A manufacturer sold a dress for \(₹720\) and made a profit of \(20\% .\) Find the cost price of a dress.
Ans:
Let the cost price of a dress be \(₹100.\)
Profit was \(20\%. \)
So, profit on \(1\) dress is \(₹20\) (because the \(CP\) is taken as \(₹100\)).
Hence, the \(SP\) of \(1\) dress \( = ₹100 + ₹20 = ₹120\)
Let the actual cost price \( = ₹x\)
Thus, \(100:120::x:720\)
\( \Rightarrow 120 \times x = 100 \times 720\)
\( \Rightarrow x = \frac{{100 \times 720}}{{120}} = ₹600\)

Profit Formula Summary

In this article, we have learned about profit, the formula of profit and how we calculate the profit. We also discussed using the profit and profit formula and solved some examples of profit formulas.
The learning outcome of this article is how the profit formulas are used to calculate the money made/ profit or loss that has been made by selling a particular product.

Solve Important Profit and Loss Questions

Frequently Asked Questions

We have provided some frequently asked questions about profit formula here:

Q.1. What is the profit percentage formula?
Ans: We can calculate the profit percentage using the following formulas:
\({\rm{Profit}}\,{\rm{Percentage}}\left( {{\rm{P}}\% } \right) = \left( {\frac{{{\rm{Profit}}}}{{{\rm{Cost}}\,{\rm{Price}}}}} \right) \times 100\)

Q.2. What is profit, and why is it important to a business?
Ans: In general, profit is important because the market price of each share and whether the business or the company is going well or not are decided by it. A profit and loss declaration also helps a company’s management team compute its net income, which is useful in business decision making.

Q.3. Do businesses calculate net profit?
Ans: Yes, all businesses calculate the net profit. Net profit consists of all the profit amount produced by the business as revenue. It signifies the actual sum of money made by any business.
Net income is a complete metric for profitability and provides an understanding of how properly the management team operates all aspects of the business.
The formula to calculate the net profit is:
\({\rm{Net}}\,{\rm{Profit}} = {\rm{Operating}}\,{\rm{Profit}} – \left( {{\rm{Taxes}}\,{\rm{and}}\,{\rm{Interest}}} \right)\)

Q.4. What is the formula for profit?
Ans: If an item’s selling price is more than the cost price, then the difference between the selling price and cost price is called profit.

Q.5. What is profit mathematically?
Ans: In mathematics, the profit depends on two things, the cost price of a product and the selling price of a product.
The amount paid to buy a product or the price at which a product is made is known as cost price. The price at which a product is sold is known as the selling price.
If \(SP > CP,\) then, \({\rm{Profit}} = SP – CP.\)

Q.6. What is the profit and loss formula?
Ans:
Profit:
If a product’s selling price is greater than its cost price, there is a profit in the business. The basic formula used for computing the profit is:
\({\rm{Profit}} = {\rm{Selling}}\,{\rm{Price}} – {\rm{Cost}}\,{\rm{Price}}.\)
Loss:
If a product’s selling price is lesser than the cost price, there is a loss in the business. The basic formula used for determining the loss is:
\({\rm{Loss}} = {\rm{Cost}}\,{\rm{Price}} – {\rm{Selling}}\,{\rm{Price}}\)

We hope this detailed article on profit formula helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!