Loss Percentage Formulas | List of Loss Percentage Formulas You Should Know - BYJUS

# Loss Percentage Formulas

When a product is sold for a price less than its original cost to the seller, we say that the product is sold at a loss, or the seller incurred a loss on the sale. This loss can be calculated as the difference between the cost price and the sale price....Read MoreRead Less

### What is Loss?

The selling price of a product or a service is the amount a customer pays to the seller to buy the product. The selling price can either be more or less as compared to the original price. When the selling price is less than the original price we say that the product is sold at a loss, or that the seller incurred a loss.

Now we could wonder what is the loss that the seller incurred?

The amount of loss incurred can be calculated using the formula to calculate loss percentage.

So let us explore this formula in detail in the next section.

### Formula for Loss Percentage

Loss is the difference between the original price and the selling price of the product, and in this case the selling price is always lower than the original price.

Loss = Original Price – Selling Price

Where, Original Price > Selling Price

When expressed as a percentage value, loss can be calculated using the formula:

Loss percentage (% Loss) = $$(\frac{\text{Loss}}{\text{Original Price}})\times 100$$

or

Loss percentage (% Loss) = $$(\frac{\text{Original Price}~-~\text{Selling Price}}{\text{Original Price}})\times 100$$

Here,

• Original price is also known as the Cost Price
• Selling Price is also known as the Sale Price

### Solved Examples

Example 1: A store owner pays $15 for a toy and sells it for$7. What is the loss incurred by the store owner in selling the toy?

Solution:

Given that,

Original price of the toy = $15. Selling price of the toy =$7.

Loss percentage (% Loss) = $$(\frac{\text{Original Price}\ -\ \text{Selling Price}}{\text{Original Price}})\times 100$$ [Formula for loss percentage]

= $$(\frac{15\ -\ 7}{15}) \times 100$$ [Substitute the given values]

= $$(\frac{8}{15})\times 100$$

= 53.33

Therefore, the store owner incurred a loss of 53.33%.

Example 2: Lucy bought an electric kettle for $50 and sold it online for$45. What is the loss Lucy incurred?

Solution:

Original Price of kettle = $50 Selling Price of Kettle =$45

Loss percentage (% Loss) = $$(\frac{\text{Original Price}\ -\ \text{Selling Price}}{\text{Original Price}})\times 100$$ [Formula for loss percentage]

= $$(\frac{50\ -\ 45}{50})\times 100$$ [Substitute the given values]

= $$(\frac{5}{50})\times 100$$

= 10

Therefore, Lucy incurred a loss of 10%.

Example 3: Rachel purchases candies in bulk for $5 per piece. She then sells them at a loss of 5%. Calculate the selling price of each candy. Solution: The details provided in the question, Original price of each candy =$5.

Percentage loss incurred = 5%

Loss percentage (% Loss) = $$(\frac{\text{Original Price}\ -\ \text{Selling Price}}{\text{Original Price}}) \times 100$$ [Formula for loss percentage]

5 = $$(\frac{5~-~\text{Selling Price}}{5}) \times 100$$              [Substitute the given values]

25 = $$(5-\text{Selling Price})\times 100$$     [Multiply both sides by 5]

0.25 = $$(5-\text{Selling Price})$$             [Divide both sides by 100]

0.25 $$-$$ 5 = $$-$$Selling Price             [Subtract 5 on both sides]

$$-$$4.75 = $$-$$Selling Price

4.75 = Selling Price                       [Multiply by $$-$$1 on both sides]

Therefore, the selling price of each candy is \$4.75.