Algebra Den


[ Home ] [ My Account ] [ Contact ]
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
Non-Collinear Points
Polygons and its Types
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Basic Geometrical Terms
Parallelogram
Triangle
Trigonometry
Trigonometry Ratios
Data-Handling
Arithmetic Mean
Graphs
Median
Mode
Range
Frequency Distribution Table
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.


Terms & Conditions

All rights reserved
Subscribe
&
Study More Algebra Topics