Area and Perimeter Definition, Formulas | How to find Area and Perimeter?

Area and Perimeter is an important and basic topic in the Mensuration of 2-D or Planar Figures. The area is used to measure the space occupied by the planar figures. The perimeter is used to measure the boundaries of the closed figures. In Mathematics, these are two major formulas to solve the problems in the 2-dimensional shapes.

Each and every shape has two properties that are Area and Perimeter. Students can find the area and perimeter of different shapes like Circle, Rectangle, Square, Parallelogram, Rhombus, Trapezium, Quadrilateral, Pentagon, Hexagon, and Octagon. The properties of the figures will vary based on their structures, angles, and size. Scroll down this page to learn deeply about the area and perimeter of all the two-dimensional shapes.

Area and Perimeter Definition

Area: Area is defined as the measure of the space enclosed by the planar figure or shape. The Units to measure the area of the closed figure is square centimeters or meters.

Perimeter: Perimeter is defined as the measure of the length of the boundary of the two-dimensional planar figure. The units to measure the perimeter of the closed figures is centimeters or meters.

Formulas for Area and Perimeter of 2-D Shapes

1. Area and Perimeter of Rectangle:

  • Area = l × b
  • Perimeter = 2 (l + b)
  • Diagnol = √l² + b²

Where, l = length
b = breadth

2. Area and Perimeter of Square:

  • Area = s × s
  • Perimeter = 4s

Where s = side of the square

3. Area and Perimeter of Parallelogram:

  • Area = bh
  • Perimeter = 2( b + h)

Where, b = base
h = height

4. Area and Perimeter of Trapezoid:

  • Area = 1/2 × h (a + b)
  • Perimeter = a + b + c + d

Where, a, b, c, d are the sides of the trapezoid
h is the height of the trapezoid

5. Area and Perimeter of Triangle:

  • Area = 1/2 × b × h
  • Perimeter = a + b + c

Where, b = base
h = height
a, b, c are the sides of the triangle

6. Area and Perimeter of Pentagon:

  • Area = (5/2) s × a
  • Perimeter = 5s

Where s is the side of the pentagon
a is the length

7. Area and Perimeter of Hexagon:

  • Area = 1/2 × P × a
  • Perimeter = s + s + s + s + s + s = 6s

Where s is the side of the hexagon.

8. Area and Perimeter of Rhombus:

  • Area = 1/2 (d1 + d2)
  • Perimeter = 4a

Where d1 and d2 are the diagonals of the rhombus
a is the side of the rhombus

9. Area and Perimeter of Circle:

  • Area = Πr²
  • Circumference of the circle = 2Πr

Where r is the radius of the circle
Π = 3.14 or 22/7

10. Area and Perimeter of Octagon:

  • Area = 2(1 + √2) s²
  • Perimeter = 8s

Where s is the side of the octagon.

Solved Examples on Area and Perimeter

Here are some of the examples of the area and perimeter of the geometric figures. Students can easily understand the concept of the area and perimeter with the help of these problems.

1. Find the area and perimeter of the rectangle whose length is 8m and breadth is 4m?

Solution:

Given,
l = 8m
b = 4m
Area of the rectangle = l × b
A = 8m × 4m
A = 32 sq. meters
The perimeter of the rectangle = 2(l + b)
P = 2(8m + 4m)
P = 2(12m)
P = 24 meters
Therefore the area and perimeter of the rectangle is 32 sq. m and 24 meters.

2. Calculate the area of the rhombus whose diagonals are 6 cm and 5 cm?

Solution:

Given,
d1 = 6cm
d2 = 5 cm
Area = 1/2 (d1 + d2)
A = 1/2 (6 cm + 5cm)
A = 1/2 × 11 cm
A = 5.5 sq. cm
Thus the area of the rhombus is 5.5 sq. cm

3. Find the area of the triangle whose base and height are 11 cm and 7 cm?

Solution:

Given,
Base = 11 cm
Height = 7 cm
We know that
Area of the triangle = 1/2 × b × h
A = 1/2 × 11 cm × 7 cm
A = 1/2 × 77 sq. cm
A = 38.5 sq. cm
Thus the area of the triangle is 38.5 sq. cm.

4. Find the area of the circle whose radius is 7 cm?

Solution:

Given,
Radius = 7 cm
We know that,
Area of the circle = Πr²
Π = 3.14
A = 3.14 × 7 cm × 7 cm
A = 3.14 × 49 sq. cm
A = 153.86 sq. cm
Therefore the area of the circle is 153.86 sq. cm.

5. Find the area of the trapezoid if the length, breadth, and height is 8 cm, 4 cm, and 5 cm?

Solution:

Given,
a = 8 cm
b = 4 cm
h = 5 cm
We know that,
Area of the trapezoid = 1/2 × h(a + b)
A = 1/2 × (8 + 4)5
A = 1/2 × 12 × 5
A = 6 cm× 5 cm
A = 30 sq. cm
Therefore the area of the trapezoid is 30 sq. cm.

6. Find the perimeter of the pentagon whose side is 5 meters?

Solution:

Given that,
Side = 5 m
The perimeter of the pentagon = 5s
P = 5 × 5 m
P = 25 meters
Therefore the perimeter of the pentagon is 25 meters.

FAQs on Area and Perimeter

1. How does Perimeter relate to Area?

The perimeter is the boundary of the closed figure whereas the area is the space occupied by the planar.

2. How to calculate the perimeter?

The perimeter can be calculated by adding the lengths of all the sides of the figure.

3. What is the formula for perimeter?

The formula for perimeter is the sum of all the sides.

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Constants and Variables Definitions | Difference Between Constants and Variables with Examples

Constants and Variables

Constants and Variables are the popular terms used in algebra. Every expression or equation will be implemented with a combination of constants and variables. Constant is a fixed value in every expression and the variables are not fixed values. Learn different problems on Constants and Variables and get a grip on the complete concept.
Example:
x^2 + 2xy + 6 is an algebraic equation.
Here, 6 cannot be changed and it is the constant number in the equation, and x^2, 2xy values are varied depends on the values. So, x^2 and 2xy are variables in the equation.

Constant & Variables – Definitions

Constant: A Constant is defined as a fixed value in algebraic expressions or equations. Constant will not change with time and has a fixed value. For instance, Shoe Size will not vary at any point.

In an algebraic expression, x+y = 5, 5 is a constant value, and will not be changed.

Variables: Variables are terms that can change or differ over time. It will not have a fixed value unlike a constant. For example, the Height and Weight of a Person will not remain constant and will vary with time.

In an algebraic expression, x+y = 5, x and y are the variables and can be varied. Go through the below modules to know more about the key differences between Constants and Variables.

Difference Between Constants and Variables

See the main differences between Constants and Variables here. ?They are along the lines

  • The main difference between the constants and variables, constant is a fixed value and a variable is not a fixed value.
  • Constants are indicated by the numerical values and the variables are indicated by any alphabetical values like a, b, c, d, ………..z.

Examples of Constants and Variables

Find the Constants and Variables of Given Expressions.

1. x + y + 2 =0.

Solution:
The given expression is x + y + 2 = 0.
Here, x and y are variables.
2 is a constant number.

2. x^2 + y^2 + 20 = 0.

Solution:
The given expression is x^2 + y^2 + 20 = 0.
Here, x^2 and y^2 are variables.
20 is a constant number.

3. xy + x^2 + 15 = 0.

Solution:
The given expression is xy + x^2 + 15 = 0.
Here, xy and x^2 are variables.
15 is a constant number.

4. 2xy + 6 = x^2y.

Solution:
The given expression is 2xy + 6 = x^2y.
Here, 2xy and x^2y are variables.
6 is a constant number.

5. x^3 + y^3 = 2xy + 8.

Solution:
The given expression is x^3 + y^3 = 2xy + 8.
Here, x^3, y^3, and 2xy are variables.
8 is a constant number.

6. Find out the constants and variables in the below questions

(i) In 5m, 5 is a constant and m is a variable.
(ii) In -3ab, -3 is a constant and a and b are variables.
(iii) In 4b, 4 is constant and b is variable but together 4b is a variable.
(iv) If 2 is a constant and a is a variable, then 2 + a, 2 – a, 2/a, 2a, a/2, etc., are also variables.

FAQs on Constants and Variables

1. What is the main difference between variables and constant?
The major difference between variables and constants is variable is a varying quantity, and a constant is a fixed value.

2. What are the variables?
The variables are the terms in an algebraic equation that can be changed or that are not fixed. Example: a + b = 8, where a and b are the variables, and 8 is a constant.

3. What are constants? 
The constants are the value in an algebraic expression that cannot be modified or changed. For example, in an equation x + y = 9, 9 is the constant value.

4. What is an algebraic expression?
The algebraic expression is a combination of constants, variables, integers, and mathematical operations.

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Common Factors Definition, Examples | How to Find Common Factors?

Common Factors

A factor is a number that is the exact multiplicand of another number. Every number factor is less than or equal to the given number but it cannot be greater than the given number. Every number has at least 2 factors. Common factors are also the factors that are common to two or more numbers. Fet the detailed steps to find the common factors of 2 or more numbers, solved examples, and applications in the below sections.

What are Common Factors?

Common Factors are defined as the factors that are common to two or more numbers. You can also say that a common factor is a number with which a set of two or more numbers will be divided exactly.

To find the common factors of two numbers, you need to list the factors of each number separately and then compare them. Now write the factors which are common and those are called common factors for the given numbers.

How to find Common Factors?

Factors are the numbers that divide the original number. Here are the steps to check whether two or more numbers have common factors or not.

  • Get the factors of each number separately.
  • Compare the factors of two numbers.
  • If you find common numbers then those are common factors between two numbers.

Example:

Common Factors of 4, 12

Find the factors of given numbers

4 = 1, 2, 4

12 = 1, 2, 3, 4, 6, 12

The common factors between 4 and 12 are 1, 2, 4.

Read More Articles,

Common Factors Examples

Example 1:

Find the common factors of 2, 16?

Solution:

The given numbers are 2, 16

Factors of 2 = 1, 2

Factors of 16 = 1, 2, 4, 8, and 16

Therefore, common factors of 2 and 16 = 1, 2.

Example 2:

Calculate the common factors of 14, 21?

Solution:

The given numbers are 14, 21

Factors of 14 = 1, 2, 7, 14

Factors of 21 = 1, 3, 7, 21

Therefore, common factors of 14 and 21 = 1, 7.

Example 3:

Find the common factors of 15, 45?

Solution:

The given numbers are 15, 45

Factors of 15 = 1, 3, 5, 15

Factors of 45 = 1, 3, 15, 5, 9, 45

Therefore, common factors of 15 and 45 = 1, 3, 5, 15.

Example 4:

Find the common factors of 36 and 63.

Solution:

The given numbers are 36, 63

The factors of 36 are

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Stop here, since the number 6 is repeated.

So, 1, 2, 3, 4, 6, 9, 12, 18, and 36 are factors of 36.

The factors of 63 are

1 × 63 = 63

3 × 21 = 63

7 × 9 = 63

9 × 7 = 63

Stop here, since the numbers 7 and 9 are repeated.

So, 1, 3, 7, 9, 21, and 63 are factors of 63.

1, 3, and 9 are common in both lists.

Hence, the common factors of 36 and 63 are 1, 3, 9.

Calculate Profit and Profit Percent – Formula, Examples | How to find Profit from Profit Percent?

Calculate Profit and Profit Percent

Calculate Profit and Profit Percent using Profit formula. Easily calculate the profit gained for a product by selling it. All the business or financial transactions are used the profit formula. The profit is calculated when the selling price of any product sold is greater than the cost price. Check out how the profit is calculated and know the profit gained by your business. We have included solved problems along with explanations.

Also, Read:

Formulas to Calculate Profit

If the selling price is more than the cost price (S.P. > C.P.), there is a profit. Various formulas to calculate profit are given below. Remember all of them for better learning.

  • Formula for Profit Profit = S.P – C.P.
  • Formula for Profit Percentage = Profit Percent Formula = (Profit x 100)/C.P.
  • Gross Profit Formula = Gross Profit = Revenue – Cost of Goods Sold
  • Profit Margin Formula = Profit Margin = (Total Income/Net Sales) x 100
  • Gross Profit Margin Formula = Gross Profit Margin = (Gross Profit/Net Sales) x 100

Notation Used in Profit Formula

  • S.P. = Selling Price i.e. the cost at which the product is sold
  • C.P. = Cost price i.e. the cost at which the product is originally bought

Profit and Profit Percent Examples

Example 1.

Ram purchased 300 calculators at $100 each. He spent $5 on packing each calculator, paid $50 to the carrying for loading, and $500 on transportation. He sold 200 at a rate of $180 each and 100 at the rate of $80 each. Find his profit or loss percent in the whole transportation.

Solution:
Given that Ram purchased 300 calculators at $100 each.
C.P. of 1 calculator = $100
C.P. of 300 calculators = $100 x 300 = $30000
Money spent on packing 1 calculator = $5
Money spent on packing 300 calculators = $300 x 5 = $1500
Overhead expenses = $(1500 + 50 + 500) = $2050
C.P. of 300 calculators = Actual C.P. + Overhead expenses
C.P. of 300 calculators = $30000 + $2050 = $32050
S.P. of 300 calculators = S.P. of 200 calculators + S.P. of 100 calculators
S.P. of 1 calculator = $180
S.P. of 200 calculators = $180 x 200 = $36000
S.P. of 1 calculator = $80
S.P. of 100 calculators = $80 x 100 = $8000
S.P. of 300 calculators = $36000 + $8000 = $44000
S. P. > C. P., there is profit, therefore, profit – S.P. – C.P.
Profit = $44000 – $32050 = $11950
Profit% = P/C.P. x 100%
Profit% = $11950/$32050 x 100%
Profit% = 37.28%

The profit percentage is 37.28%.

Example 2.

A cloth merchant bought 25 shirts, each at a price of Rs 280. He sold each of them for Rs. 300. Find his percentage profit.

Solution:
Given that a cloth merchant bought 25 shirts, each at a price of Rs 280. He sold each of them for Rs. 300.
The profit percentage remains the same for one unit as well for all the units. Thus the calculations should be done for one unit only.
The Cost Price = Rs 280
Selling Price = Rs. 300
Profit = Selling Price – Cost Price
Substitute Selling Price and Cost Price in the above formula.
Profit = Rs. 300 – Rs 280 = Rs 20.
Now, find out the profit percentage formula.
Profit percentage = P/C.P. x 100%
Profit percentage = 100 × 20/280 = 7.14%

Therefore, the profit percentage is 7.14%

Example 3.

A retail fruit vendor buys pineapples at a score of Rs. 200/-,  and retails them at a dozen for Rs 156. Did he gain or lose in the transaction and what % was his gain or loss?

Solution:
Given that a retail fruit vendor buys pineapples at a score of Rs 200, and retails them at a dozen for Rs 156.
The cost price = Rs 220
C.P/Pineapple = 200/20 = 10
1 score = 20 nos
S.P = Rs.156/dozen
S.P/Pineapple = 156/12 = 13.
Profit = Rs. 13 – Rs. 10 = Rs. 3.
% Profit = 100 × 3/10 = 30%

Therefore, the profit percentage is 30%

FAQs on Profit and Profit Percent

1. How do I calculate profit percentage?

The profit percentage can be calculated using the below formula.
Formula for Profit Percentage = Profit Percent Formula = (Profit x 100)/C.P.

2. Is profit and profit percent different?

Yes, Profit is the difference between the Selling price and the Cost price when the Selling price is more than the Cost price.
P = SP – CP; SP>CP
Profit percent will obtain by dividing the Profit with Cost price and multiplying the resultant with the 100.
Profit percent = (Profit x 100)/C.P

3. What is the formula of Selling Price?

Selling Price can be found when the Profit Percentage and Cost Price are given is
SP = {(100 + P%)/100} x CP where SP is Selling Price, P% is Profit Percentage, and CP is Cost Price.

4. How to Calculate the Percentage Gain on an Investment?

  • In calculating the percentage gain on an investment, first, determine the original cost.
  • Next, Subtract the Cost Price from the Selling price of the investment.
  • Take the gain from the investment and divide it by the original amount of the investment.
  • Finally, multiply the result by 100 to get the percentage change in the investment.

Calculate Cost Price using Sell Price and Loss Percent – Formula, Examples

Calculate Cost Price using Sell Price and Loss Percent

Loss and Loss Percent is raised when the cost price is higher than the selling price. We can calculate the Cost Price when Sell Price and Loss Percent are given. Improve your preparation by referring to the complete article. Check out how to find the Cost Price and different solved examples on finding the Cost Price using Sell Price and Loss Percent from the below article. Also, find out the different formulas to use to find the cost price.

Also, See:

How to Calculate Cost Price using Sell Price and Loss Percent?

To find out the Cost Price using Sell Price and Loss Percent, use the below formula.
Cost price = selling price + loss
Cost price = selling price + loss% × cost price/100
The Cost price – loss% × cost price/100 = selling price
Cost price(1 – loss%)/100 = selling price
Cost price(100 – loss%)/100 = selling price
Also, Cost price = selling price × 100/100 – loss% (on cross multiplication)

Examples for finding Cost Price using Sell Price and Loss Percent

1. By selling a bicycle for $145, a shopkeeper loses 10%. How much percent would he gain or lose by selling it for $175?

Solution:
Given that by selling a bicycle for $145, a shopkeeper loses 10%.
The selling price = $145
Loss Percentage = 10%
We know that cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Cost price = $145 × 100/100-10
Cost price = $145 × 100/90
The Cost price = $14500/90
Cost price = $161.11
Therefore, cost price of the bicycle = $161.11
Now, if the selling price = $175, then gain = $175 – $161.11  = $13.89
Therefore, gain% = gain/cost price × 100
= 13.89/161.11 × 100
= 1500/150
= 8.62%

Therefore, he would have gained 8.62%.

2. If the selling price of a pen is $9 and the loss percent is 2%, then what is the cost price?

Solution:
Given that the selling price of a pen is $9 and the loss percent is 2%.
The selling price of a pen = $9
The loss percent is 2%.
Cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Cost price = $9 × 100/100 – 2
Cost price = $9 × 100/98
The Cost price = $900/98 = $9.18

Therefore, the cost price of the pen is $9.18.

3. Find out the cost price of the vehicle if the selling price is $3350 and the Loss is $154.

Solution:
Given that the selling price is $3350 and the Loss is $154.
The selling price of a pen = $3350
The loss = $154
Loss = Cost Price – Selling Price
Cost Price = Loss + Selling Price
Substitute the selling price and the loss in the above formula.
Cost Price = $154 + $3350
Cost Price = $3504

Therefore, the cost price of the vehicle is $3504.

FAQs on finding C.P using S.P and Loss%

1. What Does Cost Price Mean?

The cost price is the original price of an item. The cost is the total amount need to produce a product or carry out a service.

2. What is the Formula for the Cost Price?

The formula for Cost Price when the SP and L% are given
CP = {100/(100 – L%)} x SP where SP is the Selling Price and L is the Loss.

3. What are the types of Cost Prices?

Cost Price (CP) is the amount paid to buy the product is known as Cost Price. It is denoted by CP. Also, the cost price classified into two different categories. They are
Fixed Cost: The fixed cost is constant and it doesn’t vary under any circumstances.
Variable Cost: It could change depending on the number of units.

4. How to Calculate Cost Price?

Follow the below steps and find out the process to calculate cost price when the selling price and loss% are given.
1. Note down the selling price and loss%.
2. Write the formula of cost price i.e, CP = {100/(100 – L%)} x SP
3. Substitute the SP and L% in the above formula.
4. Calculate and find the Cost Price of the product.

Calculate Loss and Loss Percent – Definition, Formulas, Examples | How to Calculate Loss Percent?

Calculate Loss and Loss Percent

Loss and Loss Percent are used for calculating the loss that occurred in a business. The loss is the difference between the cost price and the selling price. Loss Percent is the percent of loss in terms of actual cost price. The loss will occur when the selling price is less than the cost price. We have given how to Calculate Loss and Loss Percent and the formula of loss. Know the process to find them and learn how to apply them in your real life. Also, check the solved examples for a better understanding.

Do Read:

Formula to Calculate Loss and Loss Percent

The loss occurs when a cost price is more than the selling price of a product in a business. The loss is calculated by subtracting the selling price from a cost price. The formula to calculate loss and loss percentage are

  • Loss = Cost Price – Selling Price when the Cost Price is higher than the Selling Price.
    or
    Loss = C.P. – S.P. (C.P.>S.P.)
  • Loss percentage = (Loss × 100) / C.P
  • Selling Price: The Selling Price is the price of a product that was sold by the shopkeeper to the customer for a particular price. Selling price is denoted by S.P.
    Selling Price(SP)= Cost Price(CP) – Loss(L)
  • Cost Price: The cost price is the price of a product it is the original cost of a product that was brought from the retailer. Cost Price is denoted by C.P.
    Cost Price(CP)= Selling Price(SP) + Loss(L)

Loss and Loss Percent Examples

Example 1.

A shirt was bought for $300 and sold for $250. Find the loss and loss percent.

Solution:
Given that a shirt was bought for $300 and sold for $250.
The cost price = $300
Also, the selling price = $250
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = $300 – $250 = $50.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = $50/$300 × 100% = 16.66%

Therefore, the loss is $50 and the loss% is 16.66%

Example 2.

If the cost price of 30 pens is equal to the selling price of 35 pens, find a loss percent?

Solution:
Given that the cost price of 30 pens is equal to the selling price of 35 pens.
Let cost price of 1 pen = $1
Then cost price of 30 pens = $30
Also, cost price of 35 pens = $35
Since, selling price of 35 pens = cost price of 30 pens
Therefore, the selling price of 25 pens = $30
Therefore, loss = cost price – selling price
Loss = $35 – $30 = $5.
Therefore, loss% = loss/cost price × 100
loss% = $5/$35 × 100
loss% = 14.28%

Therefore, the loss is $5 and the loss% is 14.28%

Example 3.

Find the loss and loss percentage provided that the cost price is Rs. 60 and the selling price is Rs. 55.

Solution:
Given that the cost price is Rs. 60 and the selling price is Rs. 55.
The cost price = Rs. 60
Also, the selling price = Rs. 55
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = Rs. 60 – Rs. 55 = Rs. 5.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = Rs. 5/Rs. 60 × 100% = 8.33%

Therefore, the loss is Rs. 5 and the loss% is 8.33%

Example 4.

If a house was bought by a man for Rupees 60 Lakhs and he sold it in 40 Lakhs. What is a loss percentage from this business?

Solution:
Given that a house was bought by a man for Rupees 60 Lakhs and he sold it in 40 Lakhs.
The cost price = Rs. 60 Lakhs
Also, the selling price = Rs. 40 Lakhs
Since, S. P. < C. P., there is loss.
Therefore, loss = cost price – selling price
Substitute the cost price and selling price in the above formula.
Loss = Rs. 60 Lakhs – Rs. 40 Lakhs = Rs. 20 Lakhs.
So, loss% = loss/cost price × 100%
Substitute the cost price and loss in the above formula.
loss% = Rs. 20 Lakhs/Rs. 60 Lakhs × 100% = 33.33%

Therefore, the loss is Rs. 20 Lakhs and the loss% is 33.33%

FAQs on Loss and Loss Percent

1. How do you calculate percentage loss?

Follow the below steps to find the percentage loss.
1. Note down the cost price.
2. Then, check out the Selling Price, and calculate the loss.
3. Substitute the Loss and cost price in the Loss percentage formula.
4. Finally, find the Loss percentage.
Loss percentage = (Loss × 100) / C.P

2. What are the Loss and Loss Percent Formulas?

The formula for Loss and Loss Percent are
Loss = C.P. – S.P. (C.P.>S.P.)
Loss percentage = (Loss × 100) / C.P where C.P. is cost price and S.P. is selling price.

3. What is the formula for S.P when Loss and C.P. are given?

The formula for Loss = C.P. – S.P.
Therefore, S.P. = C.P. – Loss

4. How to find the C.P. when Loss and S.P. are given?

The formula for Loss = C.P. – S.P.
Therefore, C.P. = Loss + S.P.

5. How to find loss from loss percentage?

The Loss percentage = (Loss × 100) / C.P
Firstly, multiply C.P with Loss percentage and then divide it by 100 to get a Loss from the loss percentage.
Loss = (Loss percentage × C.P)/100

Calculate Cost Price using Sell Price and Profit Percent – Formula, Examples

Calculate Cost Price using Sell Price and Profit Percent

Calculate Cost Price using Sell Price and Profit Percent when the inputs are Sell Price and Profit Percent and the output is Cost Price. By simply using the Cost Price formula, one can find out the Cost Price of a product. The cost price is always less than the selling price when the profit percent is given. We have detailed explanations and solved examples are included in this article. All the different methods to find Cost Prices using Sell Price and Profit Percent are given below.

Also, Check:

How to Calculate Cost Price Using Sell Price and Profit Percent?

Follow the below process to find out the Cost Price Using Sell Price and Profit Percent. Also, get the Cost Price Formula to solve all the problems.

1. Write down the Sell Price and Profit Percent.
2. Note Down the Cost Price Formula.
3. Substitute the Sell Price and Profit Percent in the Cost Price Formula.
4. Finally, find out the Cost Price Using Sell Price and Profit Percent.

Cost Price Formula

Use the below formulas according to the problem and get the cost price easily.

Cost price = selling price – profit
Cost price = selling price – profit% × cost price/100
The Cost price + profit% × cost price/100 = selling price
Cost price(1 – profit%)/100 = selling price
Cost price(100 + profit%)/100 = selling price
Also, cost price = selling price × 100/100 + profit% (on cross multiplication);
Here, selling price and loss% is known.

Finding Cost Price Using Sell Price and Profit Percent Examples

1. A box was sold for $428 thereby gaining 8%. Find the cost price of the bag?

Solution:

Given that a box was sold for $428 thereby gaining 8%.
The selling price = $428
Gain Percentage = 8%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $428 × 100/(100 + 8)
Cost price = $428 × 100/108
The Cost price = $42800/108 = $396.29

Therefore, the cost price of the bag is $396.29

2. A fan was sold for $625 thereby gaining 15%. Find the cost price of the fan.

Solution:

Given that a fan was sold for $625 thereby gaining 15%.
The selling price = $625
Gain Percentage = 15%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $625 × 100/(100 + 15)
Cost price = $625 × 100/115
The Cost price = $62500/115= $543.47

Therefore, the cost price of the fan is $543.47

3. By selling a mobile for $1,240, a trader gains 10%. Find the cost price of the mobile?

Solution:

Given that by selling a mobile for $1,240, a trader gains 10%.
The selling price = $1,240
Gain Percentage = 10%
We know that cost price = selling price × 100/100 + gain%
Substitute the selling price and the gain% in the above formula.
Cost price = $1240 × 100/(100 + 10)
Cost price = $1240 × 100/110
The Cost price = $124000/110 = $1127.27

Therefore, the cost price of the mobile is $1127.27

Calculate Selling Price using Cost and Loss Percent – Formula, Worked Out Problems

Calculate Selling Price using Cost and Loss Percent

The amount of a thing that can be sold is known as the Selling Price. It is denoted by SP. Also, the Selling Price is also called the sale price. The selling price can be calculated when the Cost price and Loss Percent are given. Solve all the given related to Selling price problems to get a complete grip on the concept. Also, check out the given explanation of problems to find the Selling Price using Cost and Loss Percent in the later modules.

Also, See:

How to Calculate Selling Price Using Cost and Loss Percent?

Follow the complete process to find out the Selling Price Using Cost and Loss Percent. Also, know the Cost Price Formula to solve all the problems easily.

1. Note down the Cost Price and Loss Percent.
2. Write Down the Selling Price Formula.
3. Substitute the Cost Price and Loss Percent in the Selling Price Formula.
4. Finally, find out the Selling Price Using Cost Price and Loss Percent.

Selling Price Formula when Cost and Loss Percent are Known

You can use the below formula to find the Selling Price of a product when you know the Cost and Loss Percent of that product. The formulas for Selling Price Formula when Cost and Loss Percent Known are

  • Selling price = cost price – loss
  • Selling price = cost price – loss% × cost price/100
  • Selling price = 100 × cost price – loss% × cost price/100
  • Selling price = (100 – loss%)cost price/100, [Here, cost price and loss% are known.]

Solved Examples to Find Selling Price using Cost and Loss Percent

1. Sam bought a dress for $250 and sold it to Olivia thereby suffering a loss of 10%. Find the selling price of the dress?

Solution:
Given that Sam bought a dress for $250 and sold it to Olivia thereby suffering a loss of 10%.
The cost price = $250
Loss Percentage = 10%
We know that selling price = (100 – loss%) cost price/100
Substitute the cost price and the loss% in the above formula.
Selling price = (100 – 10)250/100
Selling price = 90 × 250/100
The Selling price = $22500/100 = $225

Therefore, the Selling price of the dress is $225

2. Alex bought a laptop for $600 and sold it to Jack thereby suffering a loss of 12%. Find the selling price of the laptop?

Solution:
Given that Alex bought a laptop for $600 and sold it to Jack thereby suffering a loss of 12%.
The cost price = $600
Loss Percentage = 12%
We know that selling price = (100 – loss%) cost price/100
Substitute the cost price and the loss% in the above formula.
Selling price = (100 – 12)600/100
Selling price = 88 × 600/100
The Selling price = $52800/100 = $528

Therefore, the Selling price of the dress is $528

3. By selling a table for $630, Daisy loses 7%. At what price must she sell it to gain 10%.

Solution:
Given that By selling a table for $630, Daisy loses 7%.
Given that the selling price = $ 630
Loss % = 7%
We know, cost price = selling price × 100/100 – loss%
Substitute the selling price and the loss% in the above formula.
Therefore, cost price = 630 × 100/(100 – 7)
= 630 × 100/93
= $677.41
Now cost price = $677.41
Gain% = 10%
Therefore, selling price = (100 + gain%)cost price/100
= (100 + 10)677.41/100
= 110 × 6.77
= $744.7

At $744.7 price she can sell it to gain 10%.

Circumference and Area of Circle | How to Calculate Circumference and Area of a Circle?

In Mensuration the circumference and area of a circle are defined as the length of the boundary of the circle and region occupied by the circle in 2-D Geometry. Let us discuss in detail the area and circumference of the circle using the formulas and solved example problems. We provide a detailed explanation of how to calculate the circumference and area of the circle.

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What is Circumference and Area of Circle?

Circumference of Circle:

The circumference of the circle is the measure of the boundary of the circle. The circumference of the circle is also known as the perimeter of the circle. The perimeter or circumference of the circle is measured in units.
C = Πd or 2Πr

Area of Circle:

The area of the circle is the region covered by the circle or sphere in two-dimensional mensuration. The units to measure the area of the circle is square units.
A = Πr²
Where,
A is the area of the circle
r is the radius of the circle

What is the radius of the circle?

The radius of the circle is the distance from the center to the outline of the circle. Radius plays an important role in calculating the area and perimeter of the circle.

Properties of Circle

The properties of the circle are given below,

  • The diameter of the circle is the longest chord of the circle.
  • The circle is said to be congruent if it has the same radii.
  • A circle can confine rectangle, square, trapezium, etc.
  • If the tangents are drawn at the end of the diameter they are parallel to each other.

Area and Circumference of Circle Formula

Circumference:
The circumference of the circle is the measure of the boundary of the circle. The formula for the circumference of the circle is given below,
C = Πd
Where,
C is the circumference of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
d is the diameter of the circle
C = 2Πr
Where,
C is the circumference of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
r is the radius of the circle
Area: 
The formula for the area of the circle is as follows,
A = Πr²
A is an area of the circle
Π is the mathematical constant
The approximate value of pi is 3.14 or 22/7
r is the radius of the circle
Area of Semi-Circle:
The area of the semicircle is the region covered by the 2D figure. The formula for the area of the semi-circle is as follows,
A = Πr²/2
Perimeter of the Semi-circle:
The formula for the perimeter of the semi-circle is given below,
P = 2Πr/2 = Πr

Solved Examples on Circumference and Area of a Circle?

Get the step by step explanation on the formula of Area and Circumference of Circle here.

1. What is the circumference of the circle with a radius of 7cm?

Solution:

Given,
r = 7cm
We know that,
Circumference of the circle = 2Πr
C = 2 × 22/7 × 7 cm
C = 44 cm
Thus the circumference of the circle is 44 cm.

2. What is the circumference of the circle with a diameter of 21 cm?

Solution:

Given,
d = 21 cm
We know that,
Circumference of the circle = 2Πr
C = Πd
C = 22/7 × 21cm
C = 22 × 3cm
C = 66 cm
Therefore the circumference of the circle is 66 cm.

3. Find the area of the circle with a radius of 14m?

Solution:

Given,
r = 14m
We know that,
Area of Circle = Πr²
A = 22/7 × 14 × 14 sq.m
A = 22 × 2 × 14 m²
Thus the area of the circle is 616m²

4. Find the area of the circle if its circumference is 124m?

Solution:

Given,
Circumference of the circle = 124m
We know that,
Circumference of the circle = 2Πr
124m = 2Πr
Πr = 124/2
Πr = 62
r = 62 × 7/22
r = 19.72 m
Now find the area of the circle using the radius.
Area of Circle = Πr²
A = 3.14 × (19.72)²
A = 1221 sq. m
Therefore the area of the circle is 1221 sq. meters.

5. Find the area and circumference of the circle of radius 14m?

Solution:

Given,
radius = 14m
We know that,
Circumference of the circle = 2Πr
C = 2 × 22/7 × 14m
C = 2 × 22 × 2m
C = 88m
Now find the area of the circle using the radius.
Area of Circle = Πr²
A = Π(14)²
A = 22/7 × 14 × 14 sq.m
A = 22 × 2 × 14
A = 44 × 14 sq.m
A = 616 sq.m
Thus the area of the circle is 616 sq.m

FAQs on Circumference and Area of Circle

1. How to calculate the area of a circle?

The area of the circle can be calculated by the product of pi and radius squared.

2. What is the diameter of the circle?

The diameter of the circle is 2r.

3. How to calculate the circumference of the circle?

The circumference of the circle can be calculated by multiplying the diameter with pi.

Perimeter and Area of Square | How to Calculate the Perimeter and Area of a Square?

The Perimeter and Area of the Square are used to measure the length of the boundary and space occupied by the square. These are two important formulas used in Mensuration. Perimeter and Area of the Square formulas are used in the 2-D geometry.

Square is a regular quadrilateral where are the sides and angles are equal. The concepts of the Perimeter and Area Square formula, Derivation, Properties, are explained here. The solved examples with clear cut explanations are provided in this article. Students can understand how and where to use the formulas of Area and Perimeter of Square.

What is the Area and Perimeter of the Square?

Area of a square: The area of the square is defined as the region covered by the two-dimensional shape. The units of the area of the square are measured in square units i.e., sq. cm or sq. m.

Perimeter of a square: The perimeter of the square is a measure of the length of the boundaries of the square. The units of the perimeter are measured in cm or m.

Area of Square Formula

The area of the square is equal to the product of the side and side.
Area = Side ×  Side sq. units
A = s² sq. units

Perimeter of Square Formula

The perimeter of the square is the sum of the lengths.
P = s + s + s +s
P = 4s units
Where s is the side of the square.

Diagonal of Square Formula

The square has two diagonals with equal lengths. The diagonal of the square is greater than the sides of the square.

  • The relationship between d and s is d = a√2
  • The relationship between d and Area is d = √2A

What is Square?

A square is a regular polygon in which all four sides are equal. The measurement of the angles of the square is also equal.

Properties of Squares

The properties of the square are similar to the properties of the rectangle. Go through the properties of squares from the below section.

  • All sides of the squares are equal.
  • It has 4 sides and 4 vertices.
  • The interior angles of the square are equal to 90º
  • The diagonlas of square bisect at 90º
  • The diagonals of the square are divided into two isosceles triangles.
  • The opposite sides of the squares are parallel to each other.
  • Each half of the square is equal to two rectangles.

Solved Problems on Perimeter and Area of Square

Below we have provided the solved examples of perimeter and area of a square with a brief explanation. Scroll down this page to check out the formulas of Area and Perimeter of Square.

1. What is the Area and Perimeter of the square if one of its sides is 4 meters?

Solution:

Given the side of the square is 4 meters.
Area of the square = s × s
A = 4 m × 4 m
A = 16 sq. meters
The perimeter of the square = 4s
P = 4 × 4 m
P = 16 meters.
Therefore the area and perimeter of the square are 16 sq. meters and 16 meters.

2. Find the area of the square if the side is 10 cm?

Solution:

Given,
s = 10 cm
Area of the square = s × s
A = 10 cm × 10 cm
A = 100 sq. cm
Therefore the area of the square is 100 sq. cm

3. The perimeter of the square is 64 cm. Find the area of the square?

Solution:

Given,
The perimeter of the square is 64 cm
P = 4s
64 cm = 4s
s = 64/4 = 16 cm
Thus the side of the square is 16 cm.
Now the find the area of the square.
Area of the square = s × s
A = 16 cm × 16 cm
A = 256 sq. cm
Therefore the area of the square is 256 sq. cm.

4. If the area of the square is 81 cm², then what is the length of the square?

Solution:

Given,
A = 81 cm²
Area of the square = s × s
81 sq. cm = s²
s² = 81 sq. cm
s = √81 sq. cm
s = 9 cm
Thus the length of the square is 9 cm.

5. The length of the square is 25 cm. What is the area of the square?

Solution:

Given,
The length of the square is 25 cm
Area of the square = s × s
A = 25 × 25
A = 625 sq. cm
Therefore the area of the square is 625 sq. cm.

FAQs on Perimeter and Area of Square

1. How to find the perimeter of the square?

Add all the sides of the square to find the perimeter of the square.

2. What is the formula for the perimeter of a square?

The Perimeter of Square formula is sum of the lengths i.e, side + side + side + side = 4s

3. What is the formula for the area of the square?

The area of the square formula is the product of side and side. A = s × s.

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Problems on Calculating Speed | Speed Questions and Answers

Solve different types of problems on calculating speed and get acquainted with various models of questions asked in your exams. Be aware of the Formula to Calculate and Relationship between Speed Time and Distance. Practice Speed Problems on a regular basis so that you can be confident while attempting the exams. We even provided solutions for all the Questions provided and explained everything in detail for better understanding. Try to solve the Speed Questions on your own and then cross-check where you are lagging.

We know the Speed of the Object is nothing but the distance traveled by the object in unit time.

Formula to find out Speed is given by Speed = Distance/Time

Word Problems on Calculating Speed

1.  A man walks 25 km in 6 hours. Find the speed of the man?

Solution:
Distance traveled = 25 km
Time taken to travel = 6 hours
Speed of Man = Distance traveled/Time taken
= 25km/6hr
= 4.16 km/hr
Therefore, a man travels at a speed of 4.16 km/hr

2. A car covers a distance of 420 m in 1 minute whereas a train covers 70 km in 30 minutes. Find the ratio of their speeds?

Solution:
Speed of the Car = Distance Traveled/Time Taken
= 420m/60 sec
= 7 m/sec

Speed of the Train = Distance Traveled/Time Taken
= 70 km/1/2 hr
= 140 km/hr

To convert it into m/sec multiply with 5/18
= 140*5/18
= 38.8 m/sec
= 39 m/sec (Approx)
Ratio of Speeds = 7:39

3. A car moves from A to B at a speed of 70 km/hr and comes back from B to A at a speed of 40 km/hr. Find its average speed during the journey?

Solution:
Since the distance traveled is the same the Average Speed= (x+y)/2 where x, y are two different speeds
Substitute the Speeds in the given formula
Average Speed = (70+40)/2
= 110/2
= 55 km/hr
The Average Speed of the Car is 55 km/hr

4. A bus covers a certain distance in 45 minutes if it runs at a speed of 50 km/hr. What must be the speed of the bus in order to reduce the time of journey by 20 minutes?

Solution:
Speed = Distance/Time
50 = x/3/4
50 = 4x/3
4x = 150
x = 150/4
= 37.5 km

Now by applying the same formula we can find the speed

Now, time = 40 mins or 0.66 hr since the journey is reduced by 20 mins

S = Distance/Time
= 37.5/0.66
= 56.81 km/hr

5. Ram traveled 200 km in 3 hours by train and then traveled 140 km in 3 hours by car and 5 km in 1/2 hour by cycle. What is the average speed during the whole journey?

Solution:
Distance traveled by Train is 200 km in 3 hours
Distance Traveled by Car is 140 km in 3 hours
Distance Traveled by Cycle is 5 km in 1/2 hour
Average Speed = Total Distance/Total Time
= (200+140+5)/(3+3+1/2)
= 345/6 1/2
= 345/(13/2)”
= 345*2/13
= 53.07 km/hr

6. A train covers 150 km in 3 hours. Find its speed?

Solution:
Speed = Distance/Time
= 150 km/3 hr
= 50 km/hr
Therefore, Speed of the Train is 50 km/hr.

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Problems on Calculating Distance | Distance Word Problems with Solutions

Find the Distance Problems in which an object will travel for a certain distance in a given period of time. Learn the Formula to Calculated Distance When Time and Speed are given. Refer to Solved Problems on Calculating Distance and understand the logic behind them. You can see out Time and Distance concept to know everything in detail. Practice the questions on finding distance and get the answers too from our page. Detailed Solutions makes it easy for you to grasp the concept.

Formula to Calculate the Distance = Speed * Time

Distance Word Problems Examples

1. A train moves at a speed of 45 km/hr. How far will it travel in 30 minutes?

Solution:

Speed of the Train = 45 kmph

Time = 30 min = 1/2 hr

Distance = Speed * Time

= 45Kmph*1/2 hr

= 22.5 Km

Therefore, the train travels a distance of 22.5 km

2. If a motorist moves with a speed of 40 km/hr and covers the distance from place A to B in 2 hours, find the distance between places A and B?

Solution:

Speed = 40 km/hr

Time taken to travel from Place A to Place B = 2 hrs

Distance = Speed*Time

= 40kmph*2 hr

= 80 km

Therefore, the distance between places A and B is 80 km.

3. How much father can an interstate bus go traveling 80 km/hr rather than 50 km/hr in 3 hours?

Solution:

Distance = Speed *Time

If Speed = 80 km/hr

Time = 3 hrs

Distance = 80*3

= 240 km

If Speed = 50 km/hr

Time = 3 hrs

Distance = Speed * Time

= 50*3

= 150 km

Difference between Distances = 240 km – 150 km

= 90 km

4. Sound travels at a speed of 1100 km in one hour. How many meters will it travel in one second?

Solution:

Speed = 1100 kmph

To convert kmph to m/sec multiply with 5/18

= 1100*5/18

= 305.55 m/sec

5. A car travels at a speed of 72 km/hr. How many meters will it travel in 1 second?

Solution:

Speed = 72 km/hr

To convert kmph to m/sec multiply with 5/18

= 72*5/18

= 20 m/sec

6. Mohan drives a car at a uniform speed of 40 km/hr, find how much distance is covered in 120 minutes?

Solution:

Speed = 40 km/hr

Time = 120 minutes = 2 hrs

Distance = Speed*Time

= 40 km/hr*2 hr

= 80 km

7. A car takes 2 hours to cover a distance if it travels at a speed of 30 kmph. What should be its speed to cover the same distance in 1 hour?

Solution:

Speed = 30 kmph

Time = 2hrs

Distance = Speed*TIme

= 30 kmph*2 hr

= 60 Km

Speed = ?

Distance = 60 km

Time = 1 hr

Speed = Distance/Time

= 60 km/1 hr

= 60 kmph

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Problems on Calculating Time | Time Word Problems with Solutions

Work with the Problems on Calculating Time and learn how to find Time when Speed and Distance are given. Know the Relationship between Speed Time and Distance with the formula provided. Check Worked out Examples for Distance with Solutions and cross-check your solutions while practicing. Check different types of Time Questions followed by illustrations for a better understanding of the concepts. Practice each of the Time Word Problems provided and score better grades in the exam.

Solved Time Questions with Answers

1. A car travel 70 km in 30 minutes. In how much time will it cover 120 km?

Solution:

Speed = Distance/Time

= 70 km/1/2 hr

= 140 kmph

Speed = Distance/Time

140 kmph = 120 km/Time

Time = 120 km/140 kmph

= 0.85 hr

car takes 0.85 hr to cover the distance 120 km.

2. Vinay covers 180 km by car at a speed of 60 km/hr. find the time taken to cover this distance?

Solution:

Speed = 60 km/hr

Distance = 180 km

Speed = Distance/Time

60 km/hr = 180 km/Time

Time = 180 km/60 km/hr

= 3 hr

Vinay takes 3 hrs to cover the distance 180 km at a speed of 60 km/hr.

3. A train covers a distance of 45 km in 20 minutes. Find the time taken by it to cover the same distance if its speed is decreased by 12 km/hr?

Solution:

Distance covered by train = 45 km

Time taken = 20 min = 20/60 = 1/3 hr

Speed of the train = Distance covered/Time taken

= 45km/1/3 hr

= 135 km/hr

Reduced Speed = 135 km/hr – 12 km/hr

= 123 km/hr

Time = Distance Traveled/Speed

= 45/123

= 0.365hr

= 0.365*60 min

= 21.95 min

4. A man is walking at a speed of 5 km per hour. After every km, he takes a rest for 3 minutes. How much time will it take to cover a distance of 6 km?

Solution:

Rest time = Number of rests * time of each rest

= 5*3 minutes

= 15 minutes

Total Time Taken = Distance/Speed +Rest Time

= (6/5)*60+15 minutes

= 72+15

= 87 minutes

5. A car takes 3 hours to cover a distance if it travels at a speed of 45 mph. What should be its speed to cover the same distance in 2 hours?

Solution:

Distance = Speed *Time

= 45mph*3 hr= 135 miles

Speed = Distance/Time

= 135 miles/2 hrs

= 67.5 miles per hour

Therefore, car needs to travel at a speed of 67.5 miles per hour in order to travel a distance of 135 miles in a time of 2 hrs.

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Examples on Calculating Profit or Loss | Profit and Loss Questions and Answers

Looking for help on finding Profit and Loss Concepts? Then, you have come the right way. Here let us observe some fully solved example problems on calculating profit or loss. You can find step by step solutions to all the Profit and Loss Questions available here. Try Practicing from the Profit and Loss Problems and get acquainted with the concepts better. Learn various methods for Calculating Profit and Loss and solve related problems easily. Assess your preparation standards on the concept and concentrate on the areas you are lagging in accordingly.

Question 1:
If a manufacturer allows 40% commission on the retail price of his product, he earns a profit of 9%. What would be his profit percent if the commission is reduced by 25 percent?

Solution:

We need to find out the profit % when the given commission is reduced by 25 percent.
Given data:
According to the question consider
Cost price (C.P.) of the product = $ 100
Then, a commission of the product = $ 40
Therefore selling price (S.P.) = $ (cost price (C.P.) – commission)
= $ (100 – 40)
= $ 60
Given that profit = 9%
Therefore Cost price (C.P.) = \(\frac { 100 }{ 100+gain%} \)* S.P
So,
C.P. = $ \(\frac { 100 }{ 100+9 } \)* 60
= $ \(\frac { 6000 }{109 } \)
Now new commission = $ 15
Therefore new selling price (S.P.) = $ 100 – 15
= $ 75
Gain = S.P. – C.P.
= $ (75 – \(\frac { 6000 }{109 } \))
= $ \(\frac { 2175 }{109 } \)
Gain% = (\(\frac { Profit }{C.P. } \)*100)%

=(\(\frac { 2175 }{109 } \)*\(\frac { 109 }{6000 } \)*100)%

= 36.25 %
Hence, gain % is 36.25.
Question 2:
After getting two successive discounts, a pant with the least price of $ 200 is available at $ 125. If the second discount is 14%, find the first discount.

Solution:
Let the first discount be ‘P%’
Then, 86% of (100 – P) % of 200 = 125

\(\frac { 86 }{ 100 } \)*\(\frac { (100 – P) }{ 100 } \)*200 = 125

100-P = \(\frac {(125*100*100) }{ 200*86 } \)
100 – P = 72.67
P = 100 – 72.67
P = 27.32%
Therefore, first discount price of pant is 27.32%.
Question 3:
A women sells an article at a profit of 20%. If he had bought it at 15% less and sold it for $ 11.50 less, he would have gained 25%. Find the cost price of the article.

Solution:
Given data:
Consider cost price (C.P.) of article be ‘X’
First selling price of article ‘X’ = 120% of ‘X’

= \(\frac { 120 }{ 100 } \)*X
= \(\frac { 6 }{ 5 } \)*X
Cost price of article for ‘X’ at 75% = 75% of ‘X’
=\(\frac { 75 }{ 100 } \)*X

=\(\frac { 3 }{ 4 } \)*X
Second selling price of article ‘X’ = 125% of 3/4 * X
= \(\frac { 125 }{ 100 } \)*\(\frac { 3x }{ 4 } \)

= \(\frac { 15x }{ 16 } \)

As given the article is sold at $ 11.50 less
Therefore, selling prices are equalized to a reduced price

\(\frac { 6x }{5 } \) –\(\frac { 15x }{ 16 } \) = 11.50
\(\frac { 21x }{80 } \) = 11.50
X = $ 43.8
Almost equal to $ 44
Hence, the cost price of an article is given as $ 44.
Question 4:
A dealer sold three – fourth of his articles at a gain of 25% and the remaining at cost price. Find the profit earned by him in the whole transaction.

Solution:
A dealer sold his ¾ th quantity with a gain of 25% and the remaining ¼ that its cost price.
Given data:
Consider cost price (C.P.) of whole articles be ‘X’
Cost price (C.P.) of \(\frac { 3}{ 4} \)th quantity = $ \(\frac { 3x}{ 4} \)
Cost price (C.P.) of \(\frac { 1}{ 4} \)th quantity = $ \(\frac { x}{ 4} \)
Total selling price (S.P.) = $ ((125% of \(\frac { 3x}{ 4} \)) + \(\frac { x}{ 4} \))
= $ (\(\frac { 15x}{ 16} \) + \(\frac { x}{ 4} \))
= $ (\(\frac { 19x}{ 16} \))
Profit / Gain = S.P. – C.P.
= $ (\(\frac { 19x}{ 16} \) – x)
= $ \(\frac { 3x}{ 16} \).
Gain % = (\(\frac { gain}{ C.P. } \)*100)%

= (\(\frac {3x}{ 16 } \)*\(\frac {1}{ x } \)*100)%

= 18.75%.
Hence, the gain % of the article is 18.75%.
Question 5:
A man sold two flats for $ 775,000 each. On one he gains 18% while on the other he losses 18%. How much does he gain or lose in the whole transaction?

Solution:
In this problem he gets an equal amount of profit and loss such cases there is always a loss. Therefore the selling price (S.P.) is immaterial.
Loss % = (\(\frac {common loss and gain %}{ 10 } \))2

= (\(\frac {18 }{ 10 } \))2

= (\(\frac {324 }{ 100 } \))

= 3.24%
The total loss incurred by the person is 3.24%.
Question 6:
Pure petrol costs $ 100 per lit. After adulterating it with kerosene costing $ 50 per lit, a shopkeeper sells the mixture at the rate of $ 96 per lit, thereby making a profit of 20%. In what ratio does he mix the two?

Solution:
Here, we have two different cost prices for different mixtures and one selling price (S.P.).
Given data:
Cost price (C.P.) of petrol = $ 100 per lit
Cost price (C.P.) of kerosene = $ 50 per lit
Selling price (S.P.) of mixture = $ 96 per lit
As we have two cost prices,
Mean cost price = $(\(\frac {100 }{ 120 } \))* 96)

= $ 80 per lit.
Since they asked us to find a ratio it is easy to find out by the allegation rule
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ X item quantity of $ Y item
Mean cost
$ M
(M – Y) (X – M)
Similarly using this concept here,
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ 100 item quantity of $ 50 item
Mean cost
$ 80
(80 – 50) (100 – 80)
Therefore, required ratio = 30 : 20
= 3 : 2.

Question 7:
Find cost price (C.P.), when
1. Selling price (S.P.) = $ 50, Gain = 18%
2. Selling price (S.P.) = $ 51, Loss = 14%

Solution:
Here, we need to find cost price (C.P.) using below formulae
1. Given data
Selling price (S.P.) = $ 50 & Gain = 18%
C.P. = \(\frac { 100 + Gain%) }{ 100 } \)*S.P.

=$ \(\frac { 100 + 18 }{ 100 } \)*50= $ 59.
2. Given data
Selling price (S.P.) = $ 51, Loss = 14%

C.P. = \(\frac { 100 – Loss% }{ 100 } \)*S.P.

= $ \(\frac { 100 – 14 }{ 100 } \)*51

= $ 43.86.

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Calculate Selling Price using Cost and Profit Percent – Formula, Solved Examples

Calculate Selling Price using Cost and Profit Percent

The Selling Price is easily calculated when the Cost and Profit Percent are given. Calculate Selling Price using Cost and Profit Percent and apply them to your real-time problems. Check out the various problems and their solving methods to find the Selling Price when the Cost Price and Profit Percent are given. We have included real-life examples for your practice. Don’t miss any problems to learn the complete concept.

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How to Calculate Selling Price Using Cost and Profit Percent?

Step by step procedure is given for you to find out the Selling Price Using Cost and Profit Percent. It is really easy to find the selling price when you know the cost price and Profit Percent. Therefore, check out the procedure and follow the steps while solving problems.

1. Find out the Cost price and Profit Percent from the given problem.
2. Note down the formula of Selling Price.
3. In the next step, substitute the Cost price and Profit Percent in the formula.
4. Finally, find the selling price.

Selling Price Formula when Cost and Profit Percent are Known

The Selling Price Formula is the important thing to remember to calculate all the problems when Cost and Profit Percent are given. Without missing, anyone, remember all the formulas and use them while calculating problems.

  • Selling price = cost price + profit
  • Selling price = cost price + profit%/100 × cost price
  • The selling price = 100 × cost price + profit% × cost price/100
  • selling price = (100 + profit%)cost price/100; [Here, cost price and profit% are known.]

Solved Examples to Find the Selling Price Using Cost and Profit Percent

1. Ram bought a Colors Box for $100 and sold it at a profit of 20%. Find the selling price of the book?

Solution:
Given that Ram bought a Colors Box for $100 and sold it at a profit of 20%.
The cost price of the Colors Box = $100
Profit Percentage = 20%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 20)100/100
Selling price = 120 × 100/100
The Selling price = $120

Therefore, the Selling price of the Colors Box is $120.

2. Alex bought a music system for $180. For how much should he sell the music system to gain 10%?

Solution:
Given that Alex bought a music system for $180.
The cost price of the music system = $180
Profit Percentage = 10%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 10)180/100
Selling price = 110 × 180/100
The Selling price = $198

Therefore, the Selling price of the music system is $198.

3. Robert bought a washing machine for $800 and sold it at a profit of 4%. Find the selling price of the washing machine?

Solution:
Given that Robert bought a washing machine for $800 and sold it at a profit of 4%.
The cost price of the washing machine = $800
Profit Percentage = 4%
We know that selling price = (100 + profit%)cost price/100
Substitute the cost price and the profit% in the above formula.
Selling price = (100 + 4)800/100
Selling price = 104 × 800/100
The Selling price = $832

Therefore, the Selling price of the washing machine is $832.

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