Cost Price and Selling Price: Rates of Profit and Loss

Profit and loss are used in any business to determine the product price in the market or business. There is a cost price and a selling price for every good. 

When a person purchases an item at one price and subsequently sells it at a different price, he makes a profit or loss on the product. Let us understand the terms related to cost price and selling price, discount, marked price, profit, and loss. Let’s look at these terms individually to see what they signify.

What is cost price and Selling Price?

Cost Price

The cost price is when a merchant or retailer buys or has bought items. The total amount of money it costs a manufacturer to produce a product or offer a service is known as the cost price.

Example: If Vishu bought a book for \({\rm{Rs}}\,\,{\rm{20,}}\) this is the cost price of the book.

Cost price is written in short form as \({\rm{CP}}\)

Selling Price (SP)

The price at which a shopkeeper sells a thing or commodity to a consumer is the selling price.

A product’s or service’s selling price is the amount a buyer pays for it. The pricing is determined by how much consumers are prepared to pay, the seller is willing to accept, and how competitive the price is compared to other competitors in the market.

Example: If Vishu sold the same book for \({\rm{Rs}}\,\,{\rm{25,}}\) then \({\rm{Rs}}\,\,{\rm{25,}}\) is considered the book’s selling price.

The selling price is written in short form as SP.

Profit (Gain)

When the selling price exceeds the cost price in a transaction, we have made a profit (gain).

\({\rm{Profit}}\, = \,{\rm{selling}}\,{\rm{price}}\, – \,{\rm{cost}}\,{\rm{price}}\)

Profit Percentage (Gain Percentage)

The term “profit percentage” refers to the amount of profit or gain incurred in percentage terms.

\({\rm{Profit}}\,\% \, = \,\frac{{{\rm{profit}}}}{{{\rm{cost}}\,{\rm{price}}}} \times \,100\,\% \)

Loss

When the cost price is higher than the selling price in a transaction, we lose money.

\({\rm{Loss}}\,\, = \,\,{\rm{cost}}\,{\rm{price}}\,\, – \,\,{\rm{selling}}\,{\rm{price}}\)

Loss Percentage

The term “loss percentage” refers to the amount of loss incurred in percentage terms.

\({\rm{Loss}}\,\,\%  = \,\,\frac{{{\rm{loss}}}}{{{\rm{cost}}\,{\rm{price}}}} \times 100\)

Marked Price (MP)

Sometimes, the seller marks a higher price than the expected sale price. This price is called the marked price. The marked price is the price that the dealer has written on the article’s label. The discount offered is on the market price. It is sold at a reduced price known as the selling price after applying the discount to the market price.

Discount

Shopkeepers provide discounts to customers to reduce business competition and increase product sales. A discount is a rebate or an offer made by a retailer to encourage them to buy something. The discount is always applied to the article’s marked price.

\({\rm{Discount}}\, = \,{\rm{marked}}\,{\rm{price}}\, – \,{\rm{selling}}\,{\rm{price}}\)

\({\rm{Discount}}\,\%  = \frac{{{\rm{discount}}}}{{{\rm{marked}}\,{\rm{price}}}} \times 100\% \)

Cost Price Formulas

Some of the important formulas on cost price (CP) are listed below.

1. \({\rm{Cost}}\,{\rm{price}}\,{\rm{(CP)}}\,{\rm{ = }}\,{\rm{Selling}}\,{\rm{Price}}\,{\rm{(SP)}}\,{\rm{ – Profit(P)}}\)
2. \({\rm{Cost}}\,{\rm{price}}\,{\rm{(CP)}}\,{\rm{ = }}\,{\rm{Selling}}\,{\rm{Price}}\,{\rm{(SP)}}\, + {\rm{Loss(L)}}\)
3. \({\rm{CP}}\, = \frac{{100}}{{(100\, + {\rm{profit}}\% )}} \times {\rm{SP}}\)
4. \({\rm{CP}}\, = \frac{{100}}{{(100\, – {\rm{loss}}\% )}} \times {\rm{SP}}\)

Selling Price Formulas

Some of the important formulas on selling price (SP) are listed below.

1. \({\rm{Selling}}\,\,{\rm{price}}\,({\rm{SP}})\, = \,{\rm{Cost}}\,{\rm{price}}\,\,{\rm{(CP)}}\,\,{\rm{ + }}\,{\rm{Profit}}\,\,{\rm{(P)}}\)
2. \({\rm{Selling}}\,\,{\rm{price}}\,({\rm{SP}})\, = \,{\rm{Cost}}\,{\rm{price}}\,\,{\rm{(CP)}}\,\, – \,{\rm{Loss}}\,\,{\rm{(L)}}\)
3. \({\rm{Selling}}\,\,{\rm{price}}\,({\rm{SP}})\, = \,\left( {\frac{{100 + {\rm{profit}}\% }}{{100}}} \right)\, \times \,{\rm{Cost}}\,{\rm{price}}\)
4. \({\rm{Selling}}\,\,{\rm{price}}\,({\rm{SP}})\, = \,\left( {\frac{{100 – {\rm{loss}}\% }}{{100}}} \right)\, \times \,{\rm{Cost}}\,{\rm{price}}\)
5. \({\rm{Selling}}\,\,{\rm{price}}\,({\rm{SP}})\, = \frac{{{\rm{marked}}\,{\rm{price}}}}{{{\rm{list}}\,{\rm{price}}}}\, – {\rm{Discount}}\)

Relation Between Cost Price and Selling Price

We can decide whether the sale was profitable or not depending on the cost price and selling price.

Profit (Gain) occurs when the selling price exceeds the cost price. Loss occurs when the selling price is less than the cost price. Unless otherwise noted, profit and loss percentages are always determined on the cost price.

if \({\rm{CP}} < {\rm{SP}}\) then you made a profit.

\({\rm{Profit}}\,{\rm{ = }}\,{\rm{SP}}\,{\rm{ – }}\,{\rm{CP}}\)

If \({\rm{CP}}\,{\rm{ > }}\,{\rm{SP}}\) then you will have a loss.

\({\rm{Loss}}\,{\rm{ = }}\,{\rm{CP}}\,\,{\rm{ – }}\,{\rm{SP}}\)

If \({\rm{CP}} = {\rm{SP}}\), then there is no profit or loss.

Solved Examples

Q.1. A shopkeeper bought an article at \(Rs\,50\) and sold it with a profit of \(Rs\,5\). Find the selling price of an article.
Ans: From the given \({\rm{CP}} = {\rm{Rs}}\,\,50,\,{\rm{Profit}}\,{\rm{ = }}\,{\rm{Rs}}\,{\rm{5}}\)
The formula to find the selling price is given by,
\({\rm{Selling}}\,{\rm{price}}\,({\rm{SP}})\, = \,{\rm{Cost}}\,\,{\rm{price}}\,{\rm{(CP)}}\,\,{\rm{ + }}\,\,{\rm{profit}}\,\,{\rm{(P)}}\)
\({\rm{Selling}}\,{\rm{price}}\,({\rm{SP}})\,\, = \,\,50\,\, + \,\,5\,\, = \,\,{\rm{Rs}}\,\,55\)
Therefore, the selling price of the article is \({\rm{Rs}}\,\,{\rm{55}}.\)

Q.2. Sharu sells a washing machine for \({\rm{Rs}}\,\,12{\rm{500}}\) He loses \(20\% \) in the bargain. What was the price at which he bought it?
Ans: From the given information, \({\rm{SP}}\,{\rm{ = }}\,{\rm{Rs}}\,\,{\rm{12500,}}\,{\rm{Loss}}\,{\rm{\% }}\,{\rm{ = }}\,{\rm{20}}\,{\rm{\% }}\)
\({\rm{CP}} = \frac{{100}}{{(100 – 20)}} \times 12500\)
\({\rm{CP}} = \frac{{100}}{{80}} \times 12500\)
\({\rm{CP}} = 1.25 \times 12500\)
\({\rm{CP}} = {\rm{Rs}}\,15625\)
Therefore, the cost price of the washing machine given by Sharu was \({\rm{Rs}}\,15625.\)

Q.3. A seller sells a washing machine at a cost price of Rs \(18000\) with a profit of \(10\% .\) Calculate the price at which the customer will purchase it. And also, find profit earned by the shopkeeper.
Ans: From the given, \({\rm{C}}{\rm{.P}}\,{\rm{ = }}\,{\rm{Rs}}\,{\rm{18000,}}\,{\rm{Profit\% }}\,{\rm{ = }}\,{\rm{10\% }}\)
\({\rm{Profit}}\,{\rm{ = }}{\rm{C}}{\rm{.P}} \times {\rm{Rs}}\,\,{\rm{18000,}}\,\,{\rm{Profit}}\,\,{\rm{\% }}\,\,{\rm{ = }}\,\,{\rm{10}}\,{\rm{\% }}\)
\({\rm{Profit}}\,{\rm{ = }}{\rm{18000}} \times \,\frac{{10}}{{100}}\,\)
\({\rm{Profit}}\,{\rm{ = }}{\rm{Rs}}{\rm{1800}}\,\)
\({\rm{Selling}}\,{\rm{price}} = {\rm{Profit}} + {\rm{C}}{\rm{.P}}\)
\({\rm{Selling}}{\rm{price}} = 1800 + 18000\)
\({\rm{Selling}}{\rm{price}} = {\rm{Rs}}19800\)
Therefore, the shopkeeper sold the washing machine for \({\rm{Rs}}\,\,19800\) with a profit of \({\rm{Rs}}\,\,1800.\)

Q.4. The cost of a flower vase is \({\rm{Rs}}\,\,150.\) If the shopkeeper sells it at a loss of \(10\,\% \) find the price at which it is sold.
Ans: From the given, \({\rm{CP}} = {\rm{Rs}}\,{\rm{150,}}\,{\rm{Loss}}\,{\rm{\% }}\,\,{\rm{ = }}{\rm{10\% }}\)
Loss of \(10\% \) of the cost price \( = 10\% \,{\rm{of}}\,{\rm{Rs}}\,{\rm{150}}\)
\( = \frac{{10}}{{100}}\, \times \,150\, = \,{\rm{Rs}}\,\,15\)
Then,
\({\rm{Selling}}\,{\rm{price}}\, = \,{\rm{Cost}}\,\,{\rm{price}}\)
\({\rm{Selling pricce  = }}\,{\rm{150}}\, – \,15\, = \,{\rm{Rs}}\,\,135\)
Therefore, the selling price of the vase is \({\rm{Rs}}\,\,135\).

Q.5. An item was sold for \({\rm{Rs}}\,760\) Loss is \(5\,\% .\) Then what is its cost price?
Ans: From the given, \({\rm{SP}}\, = \,{\rm{Rs}}\,760,\,{\rm{Loss}}\,\% \, = \,5\% \)
Let the cost price be \({\rm{Rs}}\,x\).
So, loss \({\rm{ = }}\,{\rm{Rs}}x \times \,\frac{5}{{100}}= {\rm{Rs}}\,\frac{x}{{20}}\)
So, the selling price is \({\rm{ = }}\,x – \frac{x}{{20}} = \,{\rm{Rs}}\,\frac{{19x}}{{20}}\)
Hence, we have \({\rm{ = }}\frac{{19x}}{{20}}= 760\)
\( \Rightarrow \,x = 760 \times \frac{{20}}{{19}} = {\rm{Rs\, 800}}\)
Therefore, the cost price of the item is \({\rm{Rs\, 800}}\)

Q.6. Shivu buys a TV for \({\rm{Rs 10000}}\) and sell it at a profit of \(15\% \). How much money does Shivu get for it?
Ans: From the given,\({\rm{CP}}\, = {\rm{Rs}}\,\,10000,\,{\rm{Profit}}\,{\rm{\% }}\,{\rm{ = }}\,{\rm{15}}\,{\rm{\% ,}}\,{\rm{SP = ?}}\)
\({\rm{Profit}}\,{\rm{ = }}\,{\rm{C}}{\rm{.P}}\,\, \times \,{\rm{Profit}}\,{\rm{\% }}\,\)
\({\rm{Profit}}\,{\rm{ = }}\,10000\,\, \times \,\,\frac{{15}}{{100}}\)
\({\rm{Profit}}\,{\rm{ = }}\,{\rm{Rs}}\,1500\,\)
\({\rm{Selling}}\,{\rm{price}} = {\rm{Profit}}\, + \,{\rm{C}}{\rm{.P}}\)
\({\rm{Selling}}\,{\rm{price}} = 1500 + 10000\)
\({\rm{Selling}}\,{\rm{price}} = {\rm{Rs}}\,11500\)
Therefore, Shivu got \({\rm{Rs}}\,\,1500\) as profit and sold a TV for \({\rm{Rs}}\,\,11500.\)

Q.7. A shopkeeper sold an article at \({\rm{Rs}}\,\,500\) and sold it with a profit of \(8\% .\) Find the cost price of an article.
Ans: From the given, \({\rm{SP}}\, = {\rm{Rs \,500,}}\,{\rm{Profit}}\,\% \, = \,8\,\%\)
 The formula to find the cost price is given by,
\({\rm{CP}} = \frac{{100}}{{(100+ {\rm{Profit\% }})}} \times {\rm{SP}}\)
\({\rm{CP}} = \frac{{100}}{{(100 + 8)}} \times 500\)
\({\rm{CP}} = \frac{{100}}{{(108)}} \times \,500\)
\({\rm{CP}} = 462.96 \approx 463.\)
Therefore, the cost price of an article was \({\rm{Rs}}\,{\rm{463}}\).

Summary

The cost price of an item is the amount spent to purchase it or the price it is manufactured. The selling price of an item is the price at which it is sold. This article includes the definition of the cost price and the selling price, profit, profit percentage, loss and loss percentage, formulas, and the relation between the cost price and the selling price.

This article helps in better understanding the topic cost price and selling price. This article’s outcome helps in applying the suitable formulas while solving the various problems based on them.

FAQs

Q.1. What is the cost price and selling price?
Ans: The cost price of an item is the amount spent to purchase it or the price at which it is manufactured. The selling price of an item is the price at which it is sold.

Q.2. How do you calculate the selling price?
Ans: In the case of loss, the selling price is calculated as follows: \({\rm{selling}}\,{\rm{price}}\,\,{\rm{ = }}\,\,{\rm{cost}}\,{\rm{price}}\, – {\rm{loss}}\)
In the case of profit, the selling price is calculated as follows: \({\rm{selling}}\,{\rm{price}}\,\,{\rm{ = }}\,\,{\rm{cost}}\,{\rm{price}}\, + \,{\rm{profit}}\)

Q.3. What is the difference between cost price and selling price?
Ans: The cost price is the amount we spend to purchase an item at its current price. Similarly, the selling price of an item is the price at which it is sold.

Q.4. How to solve cost price and selling price?
Ans: Profit (Gain) occurs when the selling price exceeds the cost price. Loss occurs when the selling price is less than the cost price. Unless otherwise noted, profit and loss percentages are always determined on the cost price.
If \({\rm{CP}}\, < \,{\rm{SP, }}\) then you made a profit. \({\rm{Profit}}\,{\rm{ = }}\,{\rm{SP  –  CP}}\)
If \({\rm{CP}}\, > \,{\rm{SP, }}\) then you will have a loss \({\rm{CP}}\, – {\rm{SP}}\)
If \({\rm{Profit}}\,{\rm{ = }}\,{\rm{SP  –  CP}}\) then there is no profit or loss.

Q.5. What is the selling price formula?
Ans: Some of the important formulas on selling price(SP) are listed below.
1. \({\rm{Selling}}\,{\rm{price(SP)}}\,{\rm{ = }}\,{\rm{Cost}}\,{\rm{price}}\,{\rm{(CP)}}\,{\rm{ + }}\,{\rm{Profit(P)}}\)
2. \({\rm{Selling}}\,{\rm{price(SP)}}\,{\rm{ = }}\,{\rm{Cost}}\,{\rm{price}}\,{\rm{(CP)}}\, – \,{\rm{Loss(L)}}\)
3. \({\rm{Selling}}\,{\rm{price(SP)}}\,{\rm{ = }}\,\left( {\frac{{100 + {\rm{profit}}\% }}{{100}}} \right)\, \times \,{\rm{Cost}}\,{\rm{price}}\)
4. \({\rm{Selling}}\,{\rm{price(SP)}}\,{\rm{ = }}\,\left( {\frac{{100 – {\rm{loss}}\% }}{{100}}} \right)\, \times \,{\rm{Cost}}\,{\rm{price}}\)
5. \({\rm{Selling}}\,{\rm{price(SP)}}\,{\rm{ = }}\,\frac{{{\rm{Marked}}\,{\rm{price}}}}{{{\rm{List}}\,{\rm{price}}}}\, – \,{\rm{Discount}}\)

Q.6. How do you calculate the cost price?
Ans: Some of the important formulas to calculate cost price(CP) are listed below.
1. \({\rm{Cost}}\,{\rm{price (CP)}}\,{\rm{ = }}\,{\rm{Selling}}\,{\rm{Price}}\,{\rm{(SP)}}\,{\rm{ – }}\,{\rm{Profit}}\,{\rm{(P)}}\)
2. \({\rm{Cost}}\,{\rm{price (CP)}}\,{\rm{ = }}\,{\rm{Selling}}\,{\rm{Price}}\,{\rm{(SP)}}\, + \,{\rm{Loss}}\,{\rm{(L)}}\)
3. \({\rm{CP}}\,{\rm{ = }}\,\frac{{100}}{{(100 + {\rm{profit}}\,\% )}} \times {\rm{SP}}\)
4. \({\rm{CP}}\,{\rm{ = }}\,\frac{{100}}{{(100 – {\rm{loss}}\,\% )}} \times {\rm{SP}}\)

Q.7. What is the marked price?
Ans: The marked price is the price that the dealer has written on the article’s label. Sometimes the discounted price is offered by the seller. It is sold at a reduced price known as the selling price after the discount is applied to the marked price.

Q.8. What is a discount?
Ans: Shopkeepers provide discounts to customers to reduce business competition and increase product sales. A discount is a rebate or an offer made by a retailer to entice people to buy something. The discount is always applied to the article’s marked price.
\({\rm{Discount}}\,{\rm{ = }}\,{\rm{Marked}}\,{\rm{price}} – \,{\rm{Selling}}\,{\rm{price}}\)
\({\rm{Discount}}\,{\rm{\% }}\,{\rm{ =  }}\frac{{{\rm{discount}}}}{{{\rm{marked}}\,{\rm{price}}}} \times 100\% \)