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Home >> Profit and Loss >> Loss Percentage >> Find Loss Percentage (L%)
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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