Loss Percentage Formula

Loss is defined as a financial disadvantage caused when the amount of money generated by a transaction is lower than the total expenditure incurred to facilitate that transaction. It can be better explained with the help of an illustration. Akash runs a saree shop. He has recently bought ten sarees from his village for Rs. 15,000. Once he reached the city, however, no one really liked his sarees, and he was forced to bring down their prices. Finally, he could sell it for only Rs.9,000. In this way, we can say that Akash is at a loss because he had bought the sarees for a high price and sold them at a low price, thus incurring a financial loss of Rs. 6,000. 

Terms Related to Loss

  • Cost Price (CP): The cost price is the amount of money spent on making or acquiring the product. For example, when Akash bought ten sarees from his village for Rs. 15000, his cost price is Rs. 15,000.

  • Selling Price (SP): After making or acquiring a product, a businessman always aims to earn more than what he spent. However, sometimes the demand for the product is so low that he is compelled to sell them at a lower price than what he bought them for. So, in this case, Akash is selling the sarees at Rs. 9000. This is his selling price. The selling price is therefore defined as the cost at which the product is sold. It is the price the consumer (buyer) pays for the product.

  • Profit (P): A profit is incurred when the selling price is higher than the cost price. It is good for business. 

  • Loss (L): A loss is only present if the cost price is greater than the selling price in a particular transaction. Here, Akash’s cost price is higher than its selling price. So, he has incurred a loss. When he incurs a loss, the businessman loses a part of the money he spent on acquiring the product. It is bad for business. Loss can also be defined as a negative profit.  

Formula to Calculate the Loss

When the selling price is subtracted from the cost price, the resulting answer is the loss. 


Loss = Cost Price – Selling Price

L = CP - SP


If the answer to CP-SP comes as a positive integer, then we have a loss. If it is a negative integer, we have a negative loss, which is termed as profit.  

Loss Percentage 

A percentage is a way of comparing two quantities. The loss is always compared to the cost price unless it is explicitly mentioned in the question that it is being compared to the selling price. Suppose Aradhana has a 20% loss percentage. Then, she has lost Rs.20 for every Rs.100 in the cost price. 

Formula to find loss percentage

Loss percentage can be calculated using the below formula:

Loss Percentage = (Loss/Cost Price) × 100

L% = (CP-SP/CP) × 100 (or) L% = (L/CP) × 100

How to calculate the loss percentage? 

A loss incurred can be calculated using the below-mentioned steps: - 

  1. Determine the value of the sold products

  2. Calculate the average selling price for the sold items

  3. Take the difference of the cost price and the selling price. 

  4. To get the loss percentage, divide the loss amount by cost price. 

  5. Then, multiply the answer you get by 100 to get the loss percentage

Solved Examples

Example 1: A retailer bought 20 mangoes for Rs. 100. In the middle, some of them became squishy due to bad storage conditions, and he had to sell them for Rs. 60. How much is the loss he incurred per mango? What is his total loss? 

Solution:

Cost Price (20 mangoes) = Rs.100

Cost Price (1 mangoes) =100/20 = Rs. 5

Selling Price (20 mangoes)= Rs. 60

Selling Price (1 mangoes)= 60/20=Rs.3

Loss (for 1 mango)= CP-SP (one mango)

 = 5-3= Rs. 2

So, his loss per mango is Rs. 2.

Loss (20 mangoes)= CP-SP (twenty mangoes)

    = 100-60= Rs. 40

So, his total loss is Rs. 40.


Example 2: A girl buys 10 beautiful blue umbrellas for Rs. 200 each.  Four of them get damaged and are rendered useless. She sells the rest at a profit of 25% each. Does she incur a profit or a loss? Calculate the profit/loss percentage.

Solution: 

Total CP= 200 x 10 = 2000

Cost Price ( 1 umbrella) = Rs. 200

Profit Percentage = 25%

P% = (P/CP) × 100 

25 = (P/200) x 100

P = Rs. 50

P = SP-CP

SP = CP+P

SP = 200 + 50

Selling Price = Rs. 250

Total SP= 250 x 6 = Rs. 1500 


The total CP is greater than the total SP, so she has incurred a loss.


Loss (L) = CP-SP

   = 2000 - 1500

   = Rs. 500


L% = (L/CP) × 100

L%= (500/2000) x 100

L%= (1/4) x 100

L%= 25%


Therefore, the girl has incurred a loss of 25% on the total CP.


Example 3: Meera sold a bag of tomatoes for Rs. 50, on which she incurs a loss of 25%. What is the amount of money she spent while making the sculpture?

Solution: 

Loss Percentage = 25%

Selling Price= Rs. 50

CP - (25/100 of CP) = 50

(75/100) * CP = 50

(3/4) * CP= 50

CP= 50* (4/3)

CP= Rs. 66.67


Therefore, the CP of the bag of tomatoes is Rs. 66.67.


FAQ (Frequently Asked Questions)

1. Why is the Loss Percentage Calculated on the Cost Price? 

Loss percentage is calculated and compared to the cost price because usually, the business owners want to calculate the amount of money they have lost per hundred rupees they have spent while manufacturing or acquiring that particular product. If the loss percentage was calculated on the selling price, they would be able to determine how much loss they are incurring per hundred rupees spent by the customer on their product. This statistic, however, is not so valuable for them. Hence, the loss percentage calculated on the cost price.