Profit and Loss

In any business transaction, we either make a profit or incur a loss. For running a business successfully or striking a sweet deal, understanding profit and loss is very important. And that is what we will be exploring on this page.

In this mini-lesson, let us learn about the selling price and cost price, how to calculate profit, to apply the profit and loss formula in our real-life problems. 

profit and loss

You can check out the interactive examples to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.

Lesson Plan

What Is Profit and Loss?

When a person buys or purchases an article for a certain price and then sells it for a different price, he makes a profit or incurs a loss.

Cost Price Selling Price
The price at which an article is purchased (CP) The price at which an article is sold (SP)
Profit Loss
Selling Price > Cost price Selling Price <  Cost price

Example

Suppose if Marc buys a juice can for 5$ and he sells it for $8, he makes a profit of $3.

\[\begin{align}\text{CP} &= $5\\\text{SP} &= $8\\\text{PROFIT} &= $8 -$5\\&= $3\end{align}\]

If he sells the juice can for $3, he incurs a loss of $2. 

\[\begin{align}\text{CP}&= $5\\\text{SP} &=$3\\\text{LOSS} &= $5 -$3\\ &= $2\end{align}\]


Definition of Profit and Loss

Profit Formula

If the selling price of an article is greater than its cost price, it is a gain or a profit made.

SP > CP

Profit = Selling Price - Cost Price

Loss Formula

If the selling price of an article is lesser than the cost price, it is the loss incurred.

SP < CP

Loss  = Cost Price - Selling Price

Let's use these formulas and find if it is profit or loss in a few business scenarios.

profit or loss

Business CP SP PROFIT/LOSS
A shopkeeper bought an article at $30 and sold it at $25. $30 $25 Loss of $5
A book bought at $35 sold at $40.  $35 $40 Profit of $5

What Is Cost Price, Marked Price, and Selling Price?

In order to cope with the competition in business and to boost the sale of goods, shopkeepers offer discounts to customers.  

discount

Discount

The rebate or the offer given by the shopkeepers to lure the customers is called a discount.

40\(\%\) discount means for every $100 SP, the rebate offered is $40.

The customer can pay only $60 for every $100.

$40 is waived off.

Discount = Marked Price - Selling Price

If the SP of the article is $600, then at 40\(\%\) discount the customer can buy the article at the following price:

\[\begin{align}\text{40 % discount on SP} &=\dfrac{40}{100}\times 600\\\\ &= \dfrac{24000}{100}\\\\&= $240\\\\ \text{SP after discount} &= 600- 240\\\\&= $360\end{align}\]

Discount is always calculated on the Marked price of the article. 

Marked Price

It is the price set by the shopkeeper on the label of the article is called the marked price.

A particular price is set high on the article against the cost price.

\(10\%\) marked price means that for every $100 CP, the shopkeeper has increased $10. 

i.e. he has fixed the new CP that is the MP as \(100 + 10 = $110\) before offering the discount.

\(\text{Discount} \% = \dfrac{\text{Discount}}{\text{MP}}\times 100\%\)

Example

Sandra goes to shopping on sale. She finds anything she purchases is at 50% discount. 

Discount

She finds the price tag on the pantaloons as $120. 

The price before discount = $120.

The price after discount 

\[\begin{align}&= 120\times \dfrac{50}{100}\\&=  60 \\\text{Discounted price} &= $60\end{align}\]


Percentage Profit and Percentage Loss

The concept of fraction and percentage finds its applications in finding the profit and the loss.

Profit or loss is generally expressed as a percentage of the cost price. 

Use the profit formula and find the profit or loss, express it as a fraction with CP at the denominator and convert it into a profit or loss percentage.

Fraction of Profit

CP = $150 SP = $180 PROFIT = $30 FRACTION = \(\dfrac{30}{150} = \dfrac{1}{5}\)

Fraction of Loss

CP = $300 SP = $280 LOSS = $20 FRACTION = \(\dfrac{20}{300} = \dfrac{1}{15}\)

Profit Formula 

\(\text{Profit}\% = (\dfrac{\text{Profit}}{\text{CP}}) \times 100\)
CP SP PROFIT/LOSS
$450 $495 Profit =$45
 FRACTION \(\%\)
\(\dfrac{45}{450} = \dfrac{1}{10}\) Profit %\(=\dfrac{1}{10}\times 100 = 10\% \)

Loss Formula

\(\text{Loss}\% = (\dfrac{\text{Loss}}{\text{CP}}) \times 100\)
CP SP PROFIT/LOSS
$400 350$ Loss = 50$
 FRACTION \(\%\)
\(\dfrac{50}{400}= \dfrac{1}{8}\) Loss %\(=\dfrac{1}{8}\times 100 = 12 \dfrac{1}{2}\%\)

Example

If  SP = $800, MP = $1000 and SP = $900, then let's find the discount\(\%\) and the profit\(\%\) using the profit formula.

\[\begin{align}\text{Discount}\\ &= \text{MP - SP}\\ &= 1000 - 900\\ &= $100\end{align}\]

\[\begin{align}\text{Discount} \%\\\\ &= \dfrac{\text{discount}}{\text{MP}}\times 100\%\\\\ &= \dfrac{100}{1000}\times 100\%\\\\&=10\%\end{align}\]

\[\begin{align}\text{Profit}\\&= \text{SP - CP}\\&= 900 - 800\\ &= $100\end{align}\]

\[\begin{align}\text{Profit}\%\\\\&=\dfrac{\text{profit}}{\text{CP}} \times 100\%\\\\&=\dfrac{100}{800} \times 100\%\\\\&=12 \dfrac{1}{2}\%\end{align}\]

 
important notes to remember
Important Notes
  1. Profit = SP - CP
  2. Loss = CP - SP
  3. Profit/Loss % = \((\dfrac{\text{profit/loss}}{\text{CP}}) \times 100\)
  4. Discount = MP - SP
  5. Discount % = \((\dfrac{\text{Discount}}{\text{MP}}) \times 100\)

Try attempting the quiz on profit and loss percentage and check if you have mastered the skill.

 
tips and tricks
Tips and Tricks
  1. Convert fraction to percent and percent to fraction wherever necessary.
  2. Profit or loss percentage is expressed as a fraction with CP at the denominator.

Solved Examples

Example 1

 

 

On selling a table for $987, Jane loses 6 \(\%\). For how much did he purchase it?

Solution

If loss is 6\(\%\), it means that is the cost price is $100, the loss incurred is $6.

\[\begin{align}\text{Loss} &= 6 \%\\\\\text{SP} &= $987\\\\\text{SP when CP is } $100 &= \text{CP - Loss}\\\\ &=100 - 6\\\\&= $94\\\\\text{CP when SP is } 94 &= 100\\\\\text{CP when SP is } $987 &= \dfrac{100}{94}\times 987\\\\ &= $1050\end{align}\]

\(\therefore\) CP= $1050
Example 2

 

 

 Ryan buys a calculator for $720 and sells it at a loss of \(6 \dfrac{2}{3}\%\). For how much does she sell it?

Solution

\[\begin{align}\text{CP} &= $720\\\\\text{Loss} &=6 \dfrac{2}{3}\%\\\\&=\dfrac{20}{3}\%\\\\\text{SP when CP is } $100&=100-\dfrac{20}{3}\\\\&=\dfrac{300 -20}{3}\\\\&=\dfrac{280}{3}\\\\&=93.3\\\\\text{SP when CP is } $720&= \dfrac{93.3}{100}\times 720\\\\&=$671.76\end{align}\]

\(\therefore\) Selling price = $671.76
Example 3

 

 

 A trader marks his goods at 40 % above the cost price and allows a discount of 25%. Find his profit.

Solution

MP = 40% i.e. if $100 is the CP,

\[\begin{align}\text{MP} &=100 +40\\ &= $140\end{align}\]

Discount = 25% i.e. 25% of $140

\[\begin{align}\text{Discount} &= \dfrac{25}{100}\times 140\\ &= \dfrac{1}{4}\times 140\\ &= $35\end{align}\]

\[\begin{align}\text{Discount} &= \text{MP - SP}\\\\\text{SP} &= \text{MP - Discount}\\\\SP &= 140 - 25 \\\\&=$115\\\\\text{CP} &= $100\\\\\text{profit} &= \text{SP - CP}\\\\&= 115 -100 \\\\&= $15\end{align}\]

\(\therefore\) Profit = $15
Example 4

 

 

Rachael bought a sweater and saved $ 200 when a discount of 25 % was given. What was the price of the sweater before the discount?

Solution

Discount = 25 %.

This means that $25 is saved for $100.

Then $200 is saved for:

\[\begin{align}\dfrac{100}{25}\times 200 &= 4\times 200\\&= $800\end{align}\]

\(\therefore\) Price before the discount = $800
Example 5

 

 

Shawn is a merchant and he is making a tally of his profit and loss in his accounts book. Help him fill in the missing entities.

CP SP PROFIT/LOSS  %
$400 a) ___ b) Profit = 25\(%\)
c)___ $990 Loss = $220 d)  ___\(%\)

Solution

Profit = 25 \(\%\)

\[\begin{align}\text{Profit}\% &= (\dfrac{\text{profit}}{\text{CP}}) \times 100\\\\25\% &= \dfrac{\text{profit}}{400} \times 100\\\\\text{profit}&= 25\times 4 \\\\\text{profit} &= 100\\\\\text{SP} &= \text{profit + CP}\\\\&= 100+400\\\\&=$500\end{align}\]

\(\therefore\) a) SP = $500

b) Profit = $100

\[\begin{align}\text{Loss} &= $220\\\\\text{Loss} &= \text{ CP - SP}\\\\\text{CP} &= \text{Loss + SP}\\\\\text{CP} &= \text{Loss + SP} = 220 + 990 \\\\&= $1210\\\\\text{Loss}\% &= \dfrac{\text{loss}}{\text{CP}} \times 100\\\\ &= \dfrac{220}{1210} \times 100\\\\&=\dfrac{200}{11}\\\\&=18 \dfrac{2}{11}\\&= 18.18 \%\end{align}\]

\(\therefore\) c) CP = $1210

d) Loss \(\% = 18. 18 \%\)


Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 

Let's Summarize

We hope you enjoyed learning about profit and loss with interactive questions. Now, you will be able to easily solve problems on profit and loss problems in real-life, as well as find answers to questions on profit percentage, discount, and other related concepts. 

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. What is profit and loss in maths?

If you sell an article for a price higher than the price that you bought, then you acquire a profit. 

If SP > CP, it's a profit made.

If you sell an article for a price lesser than the price that you bought, then you incur a loss.

If SP < CP, it's a loss incurred.

2. What is the formula for profit and loss?

Here are the formulas for profit and loss:

Profit = selling price - cost price

Loss  = cost price - selling price

3. What are the cost price and selling price?

The price for which you buy an article is its cost price and the price for which you sell an article is its selling price.

4. What does it mean by Marked Price?

The price set by the shopkeeper before offering the discount is called the marked price.

  
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus