Maths Query
As an Amazon Associate
we earn from qualifying purchases. Disclosure.
Maths query side menu
MATHS QUERY
As an Amazon Associate
we earn from qualifying purchases. Disclosure.

Profit Loss Discount Marked Price & Calculate Percentage

Back to Percentages
Maths Query > Unit > Arithmetic > Percentages

Introduction

We do shop for our daily use products or grocery items for home use or as smallest as an attractive wrist watch. The price written on the tag of watch is a marked price.

Customers buys the watch for a price paid to shopkeeper, that price is a selling price of watch.
The shopkeeper must have bought that watch from its manufacturer for a price, that price paid by shopkeeper to manufacturer is a cost price of watch.

There arises three cases depending upon at what price shopkeeper sells the watch.

  • Case 1: Watch sold at price more than its cost price

    When shopkeeper sells the watch at price more than the price he paid when he bought it from manufacturer, then he earns extra money. The extra money he earned is a profit to shopkeeper.

  • Case 2: Watch sold at price less than its cost price

    When shopkeeper sells the watch at price less than the price he bought it for his shop, then he does not earn any money even equal to its cost price. In this case, shopkeeper is in loss.

  • Case 3: Watch sold at price equal to its cost price

    When shopkeeper sells the watch at same price as its cost price, then the shopkeeper does not earn and lose any money. This is the case of no profit and no loss.

Let’s next dive into more details of profit, loss and discount and see how they are calculated in numbers with their formulas.

Cost price

The amount of money paid to buy a product is called cost price of the product.
A shopkeeper buys a product from a manufacturer or a wholesaler. The amount paid by the shopkeeper to buy the product is cost price of the product.
It is written as C.P.

Example

A shopkeeper bought a watch to sell on his shop to customers from the manufacturer. He paid $50 to manufacturer. So, $50 is the cost price of watch for the shopkeeper.

Selling price

The amount of money at which a product is sold for is called selling price of the product.
When a shopkeeper sells a product to customer and the price at which he sells it is selling price of the product.
It is written as S.P.

Example

The shopkeeper sells the watch at $70 to customers. So, $70 is the selling price of watch.

Profit

When selling price of a product is more than its cost price, then the extra amount of money earned is called profit.
When shopkeeper sells product at more than its cost price, then he earns extra amount of money, which is a profit to the shopkeeper.
Profit is calculated as difference between the selling price and cost price of a product.

Formula

  1. Profit = SP – CP

  2. If SP and profit are given, then CP is calculated as
    CP = SP – Profit

  3. If CP and profit are given, then CP is calculated as
    SP = CP + Profit
Example

The Shopkeeper bought the watch at cost price of $50 and sells it at selling price of $70.
So, the profit made by shopkeeper can be calculated as
Here, SP = $70 and CP = $50
Profit = SP – CP
∴ Profit = 70 – 50 = 20, which is $20, a profit.

Loss

When selling price of a product is less than its cost price, then the amount of money lost is called loss.
When shopkeeper buys product at more than its selling price, then he does not earn any extra amount of money rather lose money and suffers loss.
Loss is calculated as difference between the cost price and selling price.

Formula

  1. Loss = CP – SP

  2. If CP and loss are given, then SP is calculated as
    SP = CP – Loss

  3. If SP and loss are given, then CP is calculated as
    CP = SP + Loss
Example

Let’s take another example, where shopkeeper suffers loss.
Let’s say shopkeeper sold the watch with selling price of $40, which is lesser than its cost price of $50.
So, the loss made by shopkeeper can be calculated as
Here, SP = $40 and CP = $50
Loss = CP – SP
∴ Loss = 50 – 40 = 10, which is a $10, a loss.

Overhead charges

Overhead charges are those additional charges in terms of amount of money that is paid for products before selling it. It can include labour charges, maintenance charges, freight charges or any type of taxes paid on products etc.

When a shopkeeper buys products from the manufacturer premises, he has to pay freight charges to transport the products to his place. The additional amount of money paid as freight charges is an example of overhead charges.

Example

The shopkeeper in our example, if pays an $5 as freight charges to transfer the packet from manufacturer to his shop, then $5 is counted as overhead charges paid by the shopkeeper.

Effective cost price

Effective cost price includes cost price of a product and the overhead charges paid for the product.

Formula

Effective cost price = cost price + overhead charges
Example

Again, the shopkeeper paid $5 as overhead charges to transfer the watch from manufacturer to his shop and the cost price of watch is $50.
Cost price = $50
Overhead charges = $5
Effective cost price = cost price + overhead charges
∴ Effective cost price = 50 + 5 = 55, which is $55, as effective cost price.

Profit percentage

Profit percentage is the amount of profit earned out of one hundred amount of cost price.

Formula

Profit% = Profit CP × 100

Example

The shopkeeper sells the watch with selling price of $70, whose cost price is $50.
Cost price = $50
Selling price = $70
Profit = SP – CP
∴ Profit = 70 – 50 = 20
Also, Profit% = Profit CP × 100
∴ Profit% = 20 50 × 100 = 40 , which is 40% profit.

Loss percentage

Loss percentage is the amount of loss out of one hundred amount of cost price.

Formula

Loss% = Loss CP × 100

Example

When the shopkeeper sells the watch with loss with selling price of $40, whose cost price is $50.
Cost price = $50
Selling price = $40
Loss = CP – SP
∴ Loss = 50 – 40 = 10
Also, Loss% = Loss CP × 100
∴ Loss% = 10 50 × 100 = 20 , which is 20% loss.

Marked price

Price that is written on sale tag of a product is called as marked price.
It is also called as list price or print price.

Discount

Discount is the amount deducted from the marked price to reduce its selling price.
It is written as MP.
When the shopkeeper sells a product at less than its marked price, the amount of deducted price is the discount on the product.

Formula

Discount = MP – SP
Example

If, the marked price of watch is $100 and the selling price is $70.
So, Marked price = $100
Selling price = $70
Discount = MP – SP
∴ Discount = 100 – 70 = 30, which $30 discount.

Discount percentage

Discount percentage is the amount of discount on a product out of one hundred amount of marked price.

Formula

Discount% = Discount MP × 100

Example

The shopkeeper sells the watch at selling price of $70, whereas marked price on packet is $100.
Selling price = $70
Marked price = $100
Discount = MP – SP
∴ Discount = 100 – 70 = 30
Also, Discount% = Discount MP × 100
∴ Discount% = 30 100 × 100 = 30 , which is 30% discount percentage.

Solved Examples

1) Find profit if cost price = $80 and selling price = 90.

Solution
CP = $80
SP = $90
Profit = SP - CP
= 90 - 80
= $10

1) Find loss if cost price = $200 and selling price = $150.

Solution
CP = $200
SP = $150
Loss = CP - SP
= 200 - 150
= $50

3) The cost price of a smart TV is $300. A shopkeeper earned a profit of 10%. What will be the selling price of the smart TV.

Solution
CP of smart TV = $300
Profit %age = 10%
Profit %age = Profit CP × 100
10 = Profit 300 × 100
10 = Profit 3
10 × 3 = Profit
Profit = $30

4) A woman bought a watch for $120 and sold it at a loss of 20%. Find the loss she incurred and the selling price of the watch that she sold it for.

Solution
CP of watch = $120
Loss %age = 20%
Profit %age = Loss CP × 100
20 = Loss 120 × 100
20 = Loss × 5 6
20 × 6 5 = Loss
Loss = 120 5
Loss = $24
SP of watch = CP - Loss
= 120 - 24
= $96

5) A shopkeeper offered a discount of 25% on a shirt with marked price of $60. At what price the shopkeeper is selling the shirt?

Solution
Marked price on short= $60
Discount on short = 25% of marker price
∴ Discount = 25 100 × 60
∴ Discount = 1 4 × 60
= 60 4
= $15

6) Selling price of a product on an online shopping website is $200 after 20% discount on its marked price. Find the marked price of the product.

Solution
Marked price = 100 × SP 100 - Discount %
= 100 × 200 100 - 20
= 20000 80
= $250

7) Cost price of 20 articles is equal to selling price of 15 articles. Find the profit percentage or loss percentage on one article.

Solution
Let cost price of 1 article = x
∴ Cost price of 20 articles = 20x
∵ Selling price of 15 articles = Cost price of 20 articles
∴ Selling price of 15 articles = 20x
Selling price of 1 article = 20x 15
Also, SP = ( 100 - Loss% 100 ) × CP
Let loss % = y
∴ 20x 15 = ( 100 - y 100 ) × x
20 15 = ( 100 - y 100 )
15(100 - y) = 20 × 100
1500 - 15y = 2000
- 15y = 2000 - 1500
- 15y = 500
y = - 500 15
y = - 33 1 2 %
As loss is negative which represents a profit other way around.
∴ there is a profit of 33 1 2 % on one article.

8) A trademark sticks a price label on t-shirt with 30% more than its cost price. He makes a sale offer for the t-shirt at a discount of 20%. How much profit percentage will he earn by selling one t-shirt?

Solution
Let cost price of one t-shirt = $100
As marked price of one t-shirt is 30% more than the cost price of a shirt, therefore
Marked price of one t-shirt = 100 + 100 × 30 100
= 100 + 30 = $130
Discount offered on marked price of one t-shirt = 20%
Discount = 20% × 130
= 20 100 × 130
= $26
Selling price of one t-shirt = MP - Discount
= 130 - 26
= $104
Profit = SP - CP
= 104 - 100
= $4
Profit % = Profit CP × 100
= 4 100 × 100
= 4%

Worksheet 1

Fill in the blanks

1) The price at which an article is sold is known as its ___________.

2) ___________ is the price at which an article is purchased.

3) ___________ is calculated on the cost price only.

4) The marked price is also known as ___________.

5) ___________ are added to the original cost of an article.

6) The amount deducted from the marked price is called as ___________.

7) ___________ = selling price - cost price.

8) Cost price = selling price + ___________.

9) If cost price = 700, selling price = 800, then profit = ___________.

10) If cost price = 700, overhead = 200, then total cost price = ___________.

Help iconHelp box
discount
100
selling price
overhead expenses
900
loss
profit
cost price
listed price
loss percentage

Worksheet 2

Write True or False in the boxes.

1)

Profit percentage is always calculated on the cost price.

▭
2)

Profit% = Profit SP × 100

▭
3)

When SP of an article is more than cost price, then it is sold at profit.

▭
4)

Overhead expenses are not included into actual cost price.

▭
5)

Discount is given on cost price.

▭
6)

Marked price is called as printed price.

▭
7)

Discount percentage is calculated on the marked price.

▭
8)

Marked price is the sum of selling price and discount.

▭
9)

Loss is calculated as sum of cost price and selling price.

▭
10)

SP = ( 100 - Discount% 100 ) × Discount

▭

Worksheet 3

Match the following.

1)Profitcost price - selling price
2)Selling pricemarked price - selling price
3)Lossselling price - cost price
4)Discountmarked price - discount
5)Cost priceselling price + loss

Worksheet 4

Solve the questions.

1) Find profit or loss for:

  1. Cost price = 1180, Selling price = 2000
  2. Cost price = 2000, Selling price = 1800

2) Find profit percentage or loss percentage for:

  1. Cost price = 1000, Selling price = 1200
  2. Cost price = 1500, Selling price = 1700

3) A man bought a keyboard for 3200 and sold it for 3000. Find the loss percentage.

4) A shopkeeper sold the radio whose cost price is 500 at a profit of 10%. Find the selling price of radio and and profit earned by the shopkeeper. .

5) A student bought a book for 100 and sold it further at a loss of 15%. Find the price the student sold it for.

Worksheet 5

Solve the questions.

1) Cost price = 300, profit = 10%.
Find profit.

2) Cost price = 400, loss = 5%.
Find loss.

3) Cost price = 700, profit = 15%.
Find selling price.

4) Cost price = 1000, loss = 10%.
Find selling price.

5) Selling price = 1200, loss = 5%.
Find cost price.

6) Selling price = 1000, profit = 20%.
Find cost price.

Worksheet 6

Multiple choice questions

1) If cost price is 800 and selling price is 900, then profit will be

  1. 900
  2. 100
  3. 1000
  4. 800

2) When cost price is 700 and loss is 140, then loss percentage is

  1. 10%
  2. 20%
  3. 30%
  4. 40%

3) The selling price of a book is 900 and gain is 20, then cost price of the book is

  1. 720
  2. 690
  3. 880
  4. 710

4) The cost price of a table is 800 and profit percentage is 20%, then selling price of the table will be

  1. 820
  2. 460
  3. 860
  4. 960

5) A boy bought a watch for 2000 and sold it at the loss of 15%, then the amount of loss is

  1. 100
  2. 200
  3. 250
  4. 300

6) Loss percentage and profit percentage are always calculated on the

  1. marked price
  2. cost price
  3. selling price
  4. discount

7) Discount is the amount deducted from

  1. marked price
  2. cost price
  3. selling price
  4. profit

8) When marked price is 1500 and selling price is 600, then discount percentage is

  1. 60%
  2. 50%
  3. 40%
  4. 70%

9) If marked price of an article is 600 and discount percentage is 20% then selling price is

  1. 580
  2. 720
  3. 480
  4. 620

10) The selling price of a toy is 750 and discount percentage is 35% then marked price is

  1. 885
  2. 785
  3. 800
  4. 1000
MCQ Answer Key Hide Show
1. b
2. b
3. c
4. d
5. d
6. b
7. a
8. a
9. c
10. d
Last updated on: 13-07-2024

Related chapters

Profit, Loss, Discount and Different Prices Formulas
Simple, Compound and Rate of Interest with Examples
Percentages, Convert it to Fractions & Decimals
button icon Shop Maths Books chevron-right icon New Offers chevron-right icon

Search Maths books by grade

Kindergarten
Children's
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8

Maths units list

Arithmetic
Learn topic
Algebra
Learn topic
Geometry
Learn topic
Statistics
Learn topic
Things to Remember
Learn topic
Knowledge
Learn topic

Search Maths chapters by topic

2D Shapes
Learn topic
Angles
Learn topic
Area Perimeter
Learn topic
Coordinate Geometry
Learn topic
Factorization
Learn topic
Fractions
Learn topic
Lines
Learn topic
Numbers
Learn topic