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When you buy an item from a shop, the shopowner charges some amount for an item. The price at which the shopowner sells an item is not always the same as she/he bought the item. The difference between the price at which an item is bought and sold is known as profit or loss.

Every company and business works on the fundamental concept of profit and loss. It is very important to familiarize yourself with profit and loss, not only to run a business or company but also to keep an account of your own expenditure.

Let’s understand what profit and loss are and how it is calculated and learn about the profit and loss formula.

## Profit and Loss Related Terms

When a person buys an article for a certain price and then sells it for a different price, she/he makes a profit or incurs a loss. There are various terms that are associated with this transaction, such as cost price(C.P.), selling price (S.P.), discount, marked price(or list price), profit, and loss. First, let’s start to understand these terms.

**Cost Price(C.P.):** The price at which an article is bought is called its cost price. For example, if a person buys a notebook for ₹$25$, this is called the cost price of the notebook and is abbreviated as C.P.

**Selling Price(S.P.):** The price at which an article is sold is called its selling price. For example, if a person sells the same notebook for ₹$30$, this is called the selling price of the notebook and is abbreviated as S.P.

**Profit:** When, in a transaction, the selling price is greater than the cost price, it means a person earns a profit, In the above example, the person made a profit of ₹$5$, as the selling price(₹$30$) is greater than the cost price(₹$25$) of the notebook.

**Loss:** When, in a transaction, the selling price is less than the cost price, it means a person incurs a loss, In the above example, if the person had sold the notebook for ₹$20$, then it would have been a loss of ₹$5$ for him, as S.P.(₹$20$) is less than the C.P.(₹25$) of the notebook.

**Marked Price:** Marked price is the price set by the seller on the label of the article. It is a price at which the seller offers a discount. After the discount is applied to the marked price, it is sold at a reduced price known as the selling price.

For example, you go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$. This means the marked price(or list price) of the dress is ₹$1,500$.

**Discount:** In order to boost the sale of goods, shopkeepers offer discounts to customers. The rebate or the offer given by the shopkeepers to lure the customers is called a discount. Discount is **always calculated on the marked price** of the article.

$\text{Discount} = \text{Marked Price} – \text{Selling Price}$.

For example, you go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$ and the shopowner offers to sell the dress for ₹$1,200$, then the discount on the dress is $1,500 – 1,200 =$₹$300$.

## Profit and Loss Formula

These are the important formulas that are used while solving profit and loss problems.

**Profit Formula: **If the selling price of an article is greater than its cost price, there is a profit(or gain) in the transaction. The basic formula used for calculating the profit is $\text{Profit} = \text{Selling Price} – \text{Cost Price}$ or $\text{Profit} = \text{S.P.} – \text{C.P.}$

**Profit Percentage Formula:** Many times the profit(or gain) is expressed as a percentage. The formula for profit percent or gain percent is

**Loss Formula:** If the selling price of an article is less than the cost price, there is a loss in the transaction. The basic formula used for calculating the loss is $\text{Loss} = \text{Cost Price} – \text{Selling Price}$ or $\text{Profit} = \text{C.P.} – \text{S.P.}$

**Loss Percentage Formula:** Many times the loss is expressed as a percentage. The formula for loss percent is

**Note:** Profit percent or loss percent is always calculated on the cost price (C.P.) of an item.

**Selling Price Formula:** When the cost price of an item and profit percent or loss percent is known, then the selling price of an item is calculated using the formula

**Cost Price Formula:** When the selling price of an item and profit percent or loss percent is known, then the cost price of an item is calculated using the formula

## Examples

**Ex 1:** A man purchased a bicycle for ₹$840$ and sold it for ₹$800$. Find his gain/loss percent.

C.P. of bicycle = ₹$840$

S.P. of bicycle = ₹$800$

Since, $\text{S.P.} \lt \text{C.P.}$, therefore there is a loss in the transaction.

$\text{Loss} = \text{C.P.} – \text{S.P.} = 840 – 800 = $₹ $40$.

**Ex 2:** A man purchased a television set for ₹$15,800$ and sold it for ₹$18,170$. Find his gain/loss percent.

C.P. of television set = ₹$15,800$

S.P. of television set = ₹$18,170$

Since, $\text{S.P.} \gt \text{C.P.}$, therefore there is a profit in the transaction.

$\text{Profit Percent} = \frac{\text{S.P.} – \text{C.P.}}{\text{C.P.}} \times 100 = \frac{18,170 – 15,800}{15,800} \times 100 = 15$.

Therefore, the profit percent in selling the television set is $15\%$.

**Ex 3:** A bought a tape recorder for ₹$8,000$ and sold it to B. B in turn sold it to C, each earning a profit of 20%. What is the price paid for the tape recorder by C?

C.P. for A = ₹$8,000$

Profit for A = $20\%$

S.P. for A = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 20}{100} \times 8,000 =$₹ $9,600$.

S.P. for A = C.P. for B. => C.P. for B = ₹$9,600$

Profit for B = $20\%$

S.P. for B = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 20}{100} \times 9,600 =$₹ $11,520$

The price paid by C for the tape recorder is ₹$11,520$.

**Ex 4:** Reema bought a teapot for ₹$1,200$ and a set of cups for ₹$400$. She sold teapot at a profit of $5\%$ and cups at a loss of $5\%$. Find the amount received by her.

Teapot

C.P. = ₹$1,200$

Profit = $5\%$

S.P. = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 5}{100} \times 1,200 = \frac{105}{100} \times 1,200 = $₹$1,260$

Set of cups

C.P. = ₹$400$

Loss = $5\%$

S.P. = $\frac{100 – \text{Loss} \%}{100} \times \text{C.P.} = \frac{100 – 5}{100} \times 400 = \frac{95}{100} \times 400 = $₹$380$

Therefore, total amount received by Reema = $1,260 + 380 =$₹$1,640$.

**Ex 5:** By selling an item for ₹$1,12,000$, a man loses $40\%$. At what price he would have sold the item to earn a profit of $10\%$?

S.P. = ₹$1,12,000$

Loss = $40\%$

C.P. = $\frac{100}{100 – \text{Loss} \%} \times \text{S.P.} = \frac{100}{100 – 40} \times 1,12,000 =$₹$1,86,666.67$

Profit = $10\%$

S.P. = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 10}{100} \times 1,86,666.67 = $₹ $2,05,333.33$

Therefore, the man would have sold the item at ₹ $2,05,333.33$ to gain $10\%$ profit.

**Ex 6:** How much loss percent is earned by on selling $140$ geometry boxes at the loss of S.P. of $10$ geometry boxes?

Let the S.P. of $1$ geometry box = ₹$1$

So, S.P. of $140$ geometry boxes = $1 \times 140 =$ ₹$140$

Similarly, S.P. of $10$ geometry boxes = $1 \times 10 =$ ₹$10$

Loss = S.P. of $10$ geometry boxes = ₹$10$

Also, $\text{C.P.} = \text{S.P.} + \text{Loss} = 140 + 10 = $₹$150$

$\text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100 = \frac{10}{150} \times 100 = 6 \frac{2}{3}\%$.

**Ex 7:** The cost price of $10$ tables is equal to the selling price of $5$ tables. Find the profit percent in this transaction.

Let the $\text{C.P.}$ of $1$ table = ₹$1$

So, the cost of $10$ tables = $10 \times 1 =$₹$10$

C.P. of $10$ tables = S.P. of $5$ tables => Profit = Cost of $5$ tables = $5 \times 1 =$₹$5$

$\text{Profit}\% = \frac{\text{Profit}}{\text{C.P.}} \times 100 = \frac{5}{5} \times 100 = 100\%$.

## Key Takeaways

These are the important formulas for solving problems on profit and loss

- $\text{Profit} = \text{S.P.} – \text{C.P.}$ (Profit when S.P. > C.P.)
- $\text{Loss} = \text{C.P.} – \text{S.P.}$ (Loss when S.P. < S.P.)
- $\text{Profit} \% = \frac{\text{Proft}}{\text{C.P.}} \times 100$
- $\text{Loss} \% = \frac{\text{Loss}}{\text{C.P.}} \times 100$
- $\text{S.P.} = \frac{100 + \text{Profit} \%}{100} \times \text{C.P.}$
- $\text{S.P.} = \frac{100 – \text{Loss} \%}{100} \times \text{C.P.}$
- $\text{C.P.} = \frac{100}{100 + \text{Profit} \%} \times \text{S.P.}$
- $\text{C.P.} = \frac{100}{100 – \text{Loss} \%} \times \text{S.P.}$

## Conclusion

The term ‘Profit and Loss’ is a concept that is used in various real-life problems which take place in our lives almost every day. When an item is purchased at a greater price then a profit is incurred. Similarly, if an item is purchased at a lesser price then there is a loss.

## Practice Problems

- Find the selling price of an item costing ₹$1,260$ if the loss is ₹$50$.
- Find the selling price of an item costing ₹$1,050$ if the profit percentage is $50\%$.
- A shopowner bought two sofa sets at ₹$15,000$ each and sells one at a profit of $10\%$ and the other at a loss of $10\%$. Find his overall profit or loss percent.
- A shopkeeper bought $200$ bulbs for ₹$10$ each. Out of those, $5$ bulbs were fused which he throw away. He sold the remaining at ₹ $12$ each. Find the percentage of gain or loss.
- Vimal bought a plot at ₹ $13,50,000$. He wanted an overall profit of $15\%$ but he sold one-third of the plot at a loss of $8\%$. At what price should he sell the remaining plot of land?

## Recommended Reading

- What is Unitary Method? (Meaning, Formula & Examples)
- What is Percentage – Meaning, Formula & Examples
- What is Proportion? (With Meaning & Examples)
- What is Ratio(Meaning, Simplification & Examples)
- Factors and Multiples (With Methods & Examples)
- Fractions On Number Line – Representation & Examples
- Reducing Fractions – Lowest Form of A Fraction
- Comparing Fractions (With Methods & Examples)
- Like and Unlike Fractions
- Improper Fractions(Definition, Conversions & Examples)
- How To Find Equivalent Fractions? (With Examples)
- 6 Types of Fractions (With Definition, Examples & Uses)
- What is Fraction? – Definition, Examples & Types
- Mixed Fractions – Definition & Operations (With Examples)
- Multiplication and Division of Fractions
- Addition and Subtraction of Fractions (With Pictures)

## FAQs

### What are profit and loss in math?

If an article is sold at a price higher than the price at which it was bought, there is a profit in the transaction and if an article is sold at a price lesser than the price for which it was bought, there is a loss.

In other words, we can say that if Selling Price > Cost Price, there is a profit, and if Selling Price < Cost Price, there is a loss in the transaction.

### What are the cost price and selling price?

The price at which an article is bought is called its cost price, and the price at which the article is sold is called its selling price.

### How are profit and loss calculated?

Whenever the selling price of an item is greater than the cost price of an item, then there is a profit in the transaction. The formula to calculate profit is $\text{Profit} = \text{Selling Price} – \text{Cost Price}$.

Whenever the selling price of an item is less than the cost price of an item, then there is a loss in the transaction. The formula to calculate loss is $\text{Loss} = \text{Cost Price} – \text{Selling Price}$.

### What is the profit and loss percentage formula?

Whenever the selling price of an item is greater than the cost price of an item, then there is a profit in the transaction. The formula to calculate profit percent is $\text{Profit} \% = \frac{\text{Profit}}{\text{C.P.}} \times 100$.

Whenever the selling price of an item is less than the cost price of an item, then there is a loss in the transaction. The formula to calculate loss percent is $\text{Loss} \% = \frac{\text{Loss}}{\text{C.P.}} \times 100$.