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

## Find Loss Percentage (L%)

 Profit Loss Profit Percentage Loss Percentage Discount

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.

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.