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Home >> Profit and Loss >> Loss Percentage >>

## Find Loss Percentage (L%)

 Profit Loss Profit Percentage Loss Percentage Discount

 Before you understand this topic, you are advice to read: What is Loss ? Loss can also be converted into Loss Percentage(%) and is always calculated on Cost price i.e. CP. Formula for calculation of Loss Percentage is: Loss % = ( Loss / Cost Price ) X 100 Let's understand the above Loss % formula with the help of following example: Example 1 : Shopkeeper purchased a pen for \$ 10 and sold it with a loss of \$ 2. Find Loss % ? Solution: As per the given question: Cost Price or CP of the pen = \$ 10 ..... (statement 1) Loss suffered by the shopkeeper = \$ 2 ..... (statement 2) Apply the loss% formula: Loss % = ( Loss / Cost Price ) X 100 Loss % = ( 2 / 10 ) X 100 Loss % = 0.2 X 100 Loss % = 20% Hence, shopkeeper suffers a loss of 20% Find Loss%, when values of Cost Price and Selling Price are given: In some problems you are asked to find loss%, where cost price and selling price of a commodity are given. In such cases we use the same above explained formula and the difference is only in it solution. Let's try the following example: Example 2: A shopkeeper purchased a TV for \$ 265 and sold it at \$ 250. Find the percentage of loss he suffered in this deal ? Solution: As per the given question: Cost Price - CP = \$ 265 ..... (Statement 1) Selling Price - SP = \$ 250 ..... (statement 2) And we need to calculate Loss %. But before we calculate loss %, we need to find Loss and this can be calculated with the following formula: Loss = CP - SP Put the values from statement 1 and 2 & we get: Loss = \$ 265 - \$ 250 Solve the subtraction expression on the R.H.S of the equation and we get: Loss = \$ 15 ..... (Statement 3) Now Let's find Loss %, with the help of above explained formula and we get: Loss % = ( Loss / Cost Price ) X 100 Loss % = ( 15 / 250 ) X 100 Loss % = 0.06 X 100 Loss % = 6% Hence, shopkeeper suffered a loss of 6% . Find Cost Price (CP), when values of Loss% and Loss are given: In some problems you are asked to find cost price of a commodity, where value of loss and loss% suffered by the seller are given. In such cases we use the same above explained formula and the difference is only in it solution. Let's try the following example: Example 3 : Robert purchased a mobile and sold it at a loss of \$12. Also loss% in this transaction is 6%. Find cost price of the mobile ? Solution: As per the given question: Loss = \$ 12 ..... (Statement 1) Loss % = \$ 6% ..... statement 2) And we need to calculate Cost price We use the same formula to calculate CP Loss % = ( Loss / Cost Price ) X 100 6 = ( 12 / Cost Price ) X 100 Transpose the values and we get: Cost Price = ( 12 / 6 ) X 100 Cost Price = 2 X 100 Cost Price = 200 Hence, Robert purchased the mobile for \$200. Find Loss, when values of Loss% and Cost Price (CP) are given: In some problems you are asked to find Loss which seller earns, where Cost Price of the commodity and loss% suffered by the seller are given.In such cases we use the same above explained formula and the difference is only in it solution. Let's try the following example: Example 4 : Shopkeeper purchased a shirt for \$20 and sold it at a loss% of 5%. Find the loss earns in this transaction ? Solution: As per the given question: Cost Price or CP = \$ 20 ..... (Statement 1) Loss % = 5% ..... (statement 2) And we need to calculate Loss We use the same formula to calculate CP: Loss % = ( Loss / Cost Price ) X 100 5 = ( Loss / 20 ) X 100 Transpose the values and we get: Loss = (5 X 20) / 100 Loss = 100 / 100 Loss = 1 Hence, shopkeeper suffered a loss \$1. Find Selling Price (SP), when values of Loss% and Loss are given: In some problems you are asked to find selling price of a commodity, where value of loss and loss% suffered by the seller are given. In such cases we use first find Cost Price (CP) and then Selling Price (SP) is calculated. Let's try the following example: Example 5 : Tina purchased a table and sold it at a loss of \$ 12. Also loss% in this transaction is 6%. Find selling price of the table ? Solution: As per the given question: Loss = \$ 12 ..... (Statement 1) Loss % = \$ 6% ..... (statement 2) First, we will calculate cost price and to calculate this we use the following formula: Loss % = ( Loss / Cost Price ) X 100 6 = ( 12 / Cost Price ) X 100 Transpose the values and we get: Cost Price = ( 12 / 6 ) X 100 Cost Price = 2 X 100 Cost Price = 200 ..... (statement 3) So, Cost price of the table is \$200. Now, to calculate the Selling price of the table, we use the following formula: Loss = Cost Price - Selling Price Put the values from Statement 1 and statement 3 & we get: 12 = 200 - CP Subtract 200 from both sides and we get: -188 = -CP Divide both side by (-1) and we get: 188 = CP Or we can also write it as: CP = 188 Hence, Cost price of the table is \$188. Find Selling Price (SP), when values of Loss% and Cost Price (CP) are given In some problems you are asked to find selling price of the commodity, where Cost Price of the commodity and loss% suffered by the seller are given. In such cases we first find the value of loss suffered and then selling price is calculated. Let's try the following example: Example 6 : Shopkeeper purchased a shirt for \$ 20 and sold it at a loss of 5%. Find the selling price at which the shirt was sold ? Solution: As per the given question: Cost Price or CP = \$ 20 ..... (Statement 1) Loss % = 5% ..... (statement 2) And we need to calculate Loss We use the same formula to calculate CP: Loss % = ( Loss / Cost Price ) X 100 5 = ( Loss / 20 ) X 100 Transpose the values and we get: Loss = ( 5 X 20 ) / 100 Loss = 100 / 100 Loss = 1 ..... (statement 3) Now, to calculate Selling price of the shirt; we use the following formula: Loss = Cost Price - Selling Price Put the values from above statement 1 and statement 3 & we get: 1 = 20 - SP Subtract 20 from both sides and we get: -19 =- SP Divide both side by (-1) and we get: 19 = SP Or we can also write it as; SP = 19 Hence, selling price of the shirt is \$19. Find Cost Price, when selling price and Loss% are given: In some problems you are asked to find cost price of the commodity, where selling Price of the commodity and loss% suffered by the seller are given. In such cases we first find the value of loss suffered and then Cost price is calculated. Let's try the following example: Example 7 : Selling price of car is \$ 1900. If the seller made a loss of 5%, find the cost price of car. Answer: As per given question: SP of car = \$ 1900 ..... (Statement 1) Loss% = 5% ..... (Statement 2) Firstly, find value of Loss and this can be done by using the following formula Loss % = ( Loss / Cost Price ) X 100 5 = ( Loss / Cost Price) X 100 Transpose the values and we get: Loss = ( 5 X Cost Price ) / 100 Loss = Cost Price / 20 ..... (statement 3) Now, to calculate Selling price of the shirt; we use the following formula: Loss = Cost Price - Selling Price Put the values from above statement 1 and statement 3 & we get: CP / 20 = CP - 1900 Transpose CP and we get: (CP / 20) - CP = (-1900) Solve L.H.S and we get: ( -19 CP ) / 20 = - 1900 Divide both side by ( -19 / 20 ) and we get: CP = 2000 Hence, cost price of car is \$2000.

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