Profit and Loss Formulas

Profit or Loss these terms are very often used in our daily lives. These are the terms used to identify if a deal made is profitable or not.

In simple terms, if the selling price(SP) is greater than the cost price(CP), we gain a profit. If the selling price(SP) is less than the cost price(CP), then we have a loss. 

Cost Price: The price at which we buy the product.
Selling Price: The price at which we sell the product

Now let us look into profit and loss formulas and how to calculate them

Profit

The additional amount gained by selling a purchased product at a higher rate than Cost Price is called profit.

Following is the profit formula:

Profit(P) = Selling Price(SP) – Cost Price(CP)

And profit percentage can be calculated as:

Profit% (P%)= (Profit/Cost Price) x 100

Loss

The amount incurred after selling the purchased product at a lower rate than Cost Price is Loss.

Following is the loss formula:

Loss(L)= Cost Price(CP) – Selling Price(SP) 

And loss percentage can be calculated as follows:

Loss% (L%) = (Loss/Cost Price) x 100

Important Profit and Loss Formulas

1. Profit(P) = SP – CP
2. Profit%(P%) = \(\frac{P}{CP} \cdot 100\)
3. Loss(L) = CP – SP
4. Loss%(L%) = \(\frac{L}{CP} \cdot 100\)
5. Selling Price(SP) = \(\frac{100 + P \%}{100} \cdot CP\)
6. Selling Price(SP) = \(\frac{100 – L \%}{100} \cdot CP\)
7. Selling Price(SP) = Marked Price – Discount
8. Cost Price(CP) = \(\frac{100}{100 + P \%} \cdot SP\)
9. Cost Price(CP) = \(\frac{100}{100 – L \%} \cdot CP\)

Examples

Q. If a shopkeeper buys sugar 1kg for 50inr and sells for 55inr, calculate the profit and profit%

Sol CP = 50inr
SP = 55inr
Profit = SP – CP = 55 – 50 = 5inr
Profit%     = \(\frac{P}{CP} \cdot 100\)
= \frac{5}{50} \cdot 100
= 10%.

Q. What is the book’s market price if a book costs 100inr after a 10% discount?

Sol. SP = 100
Discount = 10%
SP = MP -D
Discount(D) %     = \(\frac{D}{MP} \cdot 100\)

On Rearranging the terms, we get
D = \(\frac{D% \codt MP}{100}\)

Now using these in the SP formula for D
\(SP = MP – \frac{D% \cdot MP}{100}\)
\(SP = MP \cdot \frac{100 – D%}{100}\)
\(MP = \frac{SP \cdot 100}{100 – D%}\)
\(MP = \frac{100 \cdot 100}{100 – 10}\)
\(MP = \frac{1000}{9}\)
\(MP = 111.11 INR\)

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