Profit and Loss Percentage

Profit and Loss percentages are used to show the amount of profit and loss incurred in terms of percentage, which can be a percentage of profit or percentage of loss. Also, as we all know, that percentage is one of those methods which are used for comparison of two qualities. In our day-to-day life, we come across a lot of situations where we calculate or compare anything in "per-cent." Here are some common examples: let relate the percentage of your results; everyone compares your results with your classmates or your partners.

Profit and Loss Percentage Example

Another most common example is related to buying and selling of goods. To calculate profit or loss on an item, one has to calculate it in percentage.

So, here in this article, we are going to discuss the concepts and importance of percentage in profit and loss.

To learn the concept of profit and loss percentage, we need to memorize terminologies for sales and purchase of goods.

Cost Price (CP): The price at which the item is purchased by us is known as the cost price. It is given by CP. 

Selling Price (SP): The price at which the item/good can be sold is known as the selling price. It is denoted or given by SP. 

Note: The profit or loss of a product during the sales and purchase of an item depends completely on cost price and selling price. 

Profit Percentage 

If the cost price of an item is less than the selling price, this is the only condition for profit on the item.  

               SP > CP 

Net Profit 

The net profit can be calculated as the difference between the selling price and cost price. 

             Net Profit = SP - CP

Profit Percentage Formula 

Profit % =\[\frac{SP-CP}{CP} \times 100 = \frac{Net Profit}{CP} \times 100\]

Loss Percentage 

If the cost price of the item is more than the selling price of the item, then the item is said to be sold at a loss. 

             SP < CP 

Net Loss 

Net Loss can be calculated as the difference between the cost price and selling price. 

             Net Loss=CP−SP

Loss Percentage Formula 

The amount of loss is sometimes expressed as a percentage after it has been computed in some cases. It is a percentage that is used to express the amount of loss that has been incurred in a business transaction. When comparing two quantities, this is extremely useful. The formula for calculating loss percentages are as follows: 

Loss % = \[\frac{CP-SP}{CP}\]x100 = \[\frac{Net Loss}{CP}\]x 100 

Note- It is strictly noted that the Profit Loss percentage is calculated on the Cost Price of the item, until and unless it is mentioned to calculate the percentage on Selling Price. 

Solved Examples

Question 1.   Find whether the following transactions are in profit or loss. Also, find the profit loss percent for each case. 

(i)   A General knowledge book was bought for Rs 250 and sold for Rs 325 

(ii)  Ranveer bought a motorcycle for Rs 12,000 and sold the same for Rs 13,500 

(iii)   A cupboard bought for Rs 2,500 and sold at Rs 3,000 

(iv)  A skirt bought for Rs 250 and sold at Rs 150 

Solution:

(i) C.P = RS 250 

     S.P = Rs 325 

     Here, S.P > C.P 

     So,  

     Profit = S.P - C.P 

                = 325 - 250 

                = Rs 75 

     Profit Percentage =\[\frac{{{\text{Profit}}}}{{C.P.}} \times 100\% \]

                                     = \[\frac{{75}}{{250}} \times 100\% \]

                                     = \[\frac{{75}}{{25}} \times 10\% \]

                                     = \[\frac{{15}}{5} \times 10\% \]

                                     = 3 \[ \times \] 10%

                                     = 30%

     (ii) C.P = Rs 12,000 

           S.P = Rs 13,500 

           Here S.P > C.P 

           So, 

           Profit = S.P - C.P 

                       = Rs 13,500 - 12,000 

                       = Rs 1,500  

           Profit Percentage = \[\frac{{{\text{Profit}}}}{{C.P.}} \times 100\% \]

                                           = \[\frac{{1,500}}{{12,000}} \times 100\% \]

                                           = 15/120 \[ \times \] 100%

                                           = 15/12 \[ \times \]10%

                                           = 5/4 \[ \times \] 10%

                                           = 5/2 \[ \times \] 5%

                                           = 25/2%

                                           = 12.5%

     (iii) C.P = Rs 2,500 

            S.P = Rs 3,000 

            Here S.P > C.P 

            So, 

            Profit = S.P - C.P 

                       = Rs 3,000 - 2,500 

                       = Rs 500 

            Profit Percentage = \[\frac{{{\text{Profit}}}}{{C.P.}} \times 100\% \]

                                            = \[\frac{{500}}{{2,500}} \times \]100%

                                            = 5/25 \[ \times \] 10%

                                            = 1/5 \[ \times \]10%

                                            = 20%

     (iv) C.P = Rs 250 

            S.P = Rs 150 

            Here C.P > S.P 

            So, 

            Profit = C.P - S.P 

                       = Rs 250 - 150 

                       = Rs 100 

            Loss Percentage =\[\frac{{{\text{Loss}}}}{{C.P.}} \times 100\% \]

                                          =\[\frac{{100}}{{250}} \times \] 100%

                                          = 10/25 \[ \times \] 10%

                                          = 2/5 \[ \times \]10%

                                          = 2 \[ \times \] 20%

                                          = 40%

Question 2: Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. At what price Juhi bought the washing machine? 

Solution: 

S.P = Rs 13,500 

C.P =? 

Loss Percentage = 20% 

Now, 

 Loss = C.P - S.P 

C.P =S. P + Loss 

C.P = 13,500 + Loss           ….(i) 

Loss Percentage = \[\frac{Loss}{CP} \times 100\]%

\[\frac{20 %}{100 %} = \frac{Loss}{13,500+Loss}\]

\[\frac{20 }{100 } = \frac{Loss}{13,500+Loss}\]

\[\frac{2}{100} = \frac{Loss}{13,500+Loss}\]     

\[\frac{1}{5} = \frac{Loss}{13,500+Loss}\]                                          

Cross Multiplying

                1 \[ \times \] (13,500 + Loss) = 5\[ \times \] Loss

                13,500 + Loss = 5 Loss

                5 Loss = 13500 + Loss

                5 Loss - Loss = 13500

                4 Loss = 13500

                Loss  = \[\frac{{13,500}}{4}\]

                Loss =  Rs 3,375

From (i)

      C.P = 13500 + 3375

             = Rs 16875 

So, she bought it at Rs 16,875                             

Question 3. 2. Ron purchased a table for Rs 1260, and due to some scratches on the top of the table, Ron has to sell it for Rs 1197. Find the loss percent.  

Solution:  

CP =  Rs.1260  

SP = Rs 1197.  

Since,  

      (SP) < (CP), Ron makes a loss.  

      Loss = Rs (1260 - 1197)  

               = Rs 63.  

      Loss Percentage =  \[\frac{Loss}{C.P}\]x100%

                                    = \[\frac{63}{1260}\] ×100  

                                    = 5% 

Question 4.  A man purchases a fan for Rs. 1000 and then sells it at a loss of 15% on the sale of the fan. In what range does the fan's selling price fall?

Solution: The cost of the fan is Rs. 1000, which is the solution.

The percentage of losses is 15 percent.

As we all know, loss percentage  = (Loss/Cost Price) x 100

15 = (Loss/1000) x 100.

As a result, Loss = 150 rs.

As we are all aware,

Loss = Cost Price – Selling Price

So, Selling Price = Cost Price – Loss

= 1000 - 150

Pricing: R.850/- 

Question 5: Mukesh bought two watches at the same price and sold one at a 20% profit and the other at a 22.5 percent profit. What is the cost price of each of the watches if the difference in selling prices is Rs 150?

Solution: Let the cost of the watches be equal to 100x. 

Then the selling price of the first watch is 120x, and the selling price of the second watch is 122.5x.

The difference between selling prices is given as 150.

So, 122.5x - 120x = 150

2.5x = 150

x= 150 2.5

Therefore, x= 375

Substituting the x value in the original cost price, we get 100x = 100 (375) = Rs.37500.

Therefore the price of each watch is Rs. 37500.

Conclusion 

Profit and loss formulas are used to calculate the profit or loss generated by the sale of a specific product. A product's cost price is the price at which it is purchased. A product's selling price is the price at which it is sold. Profit is defined as the difference between the selling price and the cost price when the selling price is the more than the cost price. The difference between the selling price and the cost price is referred to as loss when the selling price is less than the cost price. When calculating profit and loss percentages for an article, it is important to remember that after purchasing the article, one may have to pay additional fees for transportation, repairing charges, local taxes, and so on. These additional costs are referred to as overheads.