### Theory:

Profit and loss are the terms related to business transactions.

Key Concepts:

1. Cost Price:
The price at which a person buys a product is called the Cost Price (C.P) of that product.
2. Selling Price:
The price at which a person sells a product is called the Selling Price (S.P) of that product.
3. Profit:
• When the selling price of a product is higher than the cost price, profit is achieved, which is equal to the difference in selling price and the cost price.
• Profit $$=$$ Selling price ($$S.P$$) $$-$$ Cost price ($$C.P$$).
When $S.P\succ C.P$ [When the $$S.P$$ is more than the $$C.P$$ then there is a profit.]

Important!
Another synonymous term is used for profit is gain.
4. Loss:
When the selling price is less than the cost price, there is a loss in the transaction, which is equal to the difference of the cost price and the selling price.
Loss$=C.P-S.P$.

When $S.P\prec C.P$ [When the $$S.P$$ is less than the $$C.P$$ then there is a loss]

Important!
It is to be noted that the profit or loss is always calculated on the cost price.
Profit and loss as a percentage:
Mahesh bought a computer worth of $$₹$$1000, and he sold it to his friend on $$₹$$1250.

In this transaction, he will get $$₹$$250 as a profit.

But can you find the profit percentage of this transaction?

We can use this formula to find the profit percentage if we know the profit and cost price of the product.

Profit $$\% =$$ $$\frac{\text{Profit}}{\text{Cost price}}$$$$\times100$$

Profit $$\% =$$ $\frac{250}{1000}×100$

$\begin{array}{l}=\frac{250}{1000}×100\\ \\ =\frac{25000}{1000}\\ \\ =25%\end{array}$

Therefore the profit percentage of this transaction is 25$$\%$$.

Measuring the profit or loss in terms of percentage is an easy and convenient method.

That is why most of the shop keepers are mention the profit or loss of their product in percentage.

We can also apply the same concept to find the original rate of the product if a certain percentage discount is applied to that product.

We will see some exercises to understand this concept better.