Arithmetic Additive Identity Associative Property Averages Brackets Closure Property Commutative Property Conversion of Measurement Units Cube Root Decimal Distributivity of Multiplication over Addition Divisibility Principles Equality Exponents Factors Fractions Fundamental Operations H.C.F / G.C.D Integers L.C.M Multiples Multiplicative Identity Multiplicative Inverse Numbers Percentages Profit and Loss Ratio and Proportion Simple Interest Square Root Unitary Method
Algebra Algebraic Equation Algebraic Expression Order Relation Standard Identities & their applications Transpose Cartesian System Linear Equations Probability Polynomials
Geometry Circle Curves Angles Define Line, Line Segment and Rays NonCollinear Points Polygons and its Types Rectangle Rhombus Square Three dimensional object Trapezium Basic Geometrical Terms Parallelogram Triangle
Trigonometry Trigonometry Ratios
DataHandling Arithmetic Mean Graphs Median Mode Range Frequency Distribution Table 
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
Lets 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. Lets 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 Lets 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. Lets 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. Lets 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. Lets 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. Lets 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. Lets 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.


