Find Profit Loss Marked Prices & Discount Percentage

Real life examples of prices

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

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

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

Case 1: Watch sold at price more than its cost price.
When a shopkeeper sells the watch at more than the price he paid when he bought it from the manufacturer, then he earns extra money. The extra money he earned is a profit to the shopkeeper.
Case 2: Watch sold at price less than its cost price.
When a shopkeeper sells the watch at 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, the shopkeeper is at a loss.
Case 3: Watch sold at price equal to its cost price.
When a shopkeeper sells the watch at the 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.

What is the cost price?

The amount of money paid to buy a product is called the 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 the cost price of the product.
It is written as C.P.

Example of cost price

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

What is the selling price?

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

Example of selling price

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

How to find profit?

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

Formula

Profit = SP - CP
If SP and profit are given, then CP is calculated as
CP = SP - Profit
If CP and profit are given, then SP is calculated as
SP = CP + Profit

Example to find profit

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.

How to find loss?

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

Formula

Loss = CP - SP
If CP and loss are given, then SP is calculated as
SP = CP - Loss
If SP and loss are given, then CP is calculated as
CP = SP + Loss

Example to find loss

Let's take another example, where a shopkeeper is at a loss.
Let's say the shopkeeper sold the watch with a selling price of $40, which is less 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.

What are overhead charges?

Overhead charges are those additional charges in terms of the 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 of overhead charges

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

Calculate effective cost price

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

Formula

Effective cost price = cost price + overhead charges

Example of effective cost price

Again, the shopkeeper paid $5 as overhead charges to transfer the watch from the manufacturer to his shop and the cost price of the 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.

Find profit percentage

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

Formula

Profit% = $\frac{Profit}{CP} \times 100$

Example to find profit percentage

The shopkeeper sells the watch with a selling price of $70, whose cost price is $50.
Cost price = $50
Selling price = $70
Profit = SP - CP
∴ Profit = 70 - 50 = 20
Also, Profit% = $\frac{Profit}{CP} \times 100$
∴ Profit% = $\frac{20}{50} \times 100$
= 40, which is 40% profit.

Find loss percentage

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

Formula

Loss% = $\frac{Loss}{CP} \times 100$

Example to find loss percentage

When the shopkeeper sells the watch at a loss with a selling price of $40, the cost price is $50.
Cost price = $50
Selling price = $40
Loss = CP - SP
∴ Loss = 50 - 40 = 10
Also, Loss% = $\frac{Loss}{CP} \times 100$
∴ Loss% = $\frac{10}{50} \times 100$
= 20, which is a 20% loss.

What is the marked price?

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

How to calculate a discount?

Discount is the amount deducted from the marked price to reduce its selling price.
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 of discount calculations

The marked price of a watch is $100 and the selling price is $70.
So, Marked price = $100
Selling price = $70
Discount = MP - SP
∴ Discount = 100 - 70 = $30

Find discount percentage

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

Formula

Discount% = $\frac{Discount}{MP} \times 100$

Example of discount percentage

The shopkeeper sells the watch at a selling price of $70, whereas the marked price on the packet is $100.
Selling price = $70
Marked price = $100
Discount = MP - SP
∴ Discount = 100 - 70 = 30
Also, Discount% = $\frac{Discount}{MP} \times 100$
∴ Discount% = $\frac{30}{100} \times 100$
= 30, which is a 30% discount percentage.

Solved Examples

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

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

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

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?

CP of smart TV = $300
Profit %age = 10%
Profit %age = $\frac{Profit}{CP} \times 100$
10 = $\frac{Profit}{300} \times 100$
10 = $\frac{Profit}{3}$
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.

CP of watch = $120
Loss %age = 20%
Loss %age = $\frac{Loss}{CP} \times 100$
20 = $\frac{Loss}{120} \times 100$
20 = $Loss \times \frac{5}{6}$
$\frac{20 \times 6}{5}$ = Loss
Loss = $\frac{120}{5}$
Loss = $24
SP of watch = CP - Loss
= 120 - 24
= $96

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

Marked price on shirt= $60
Discount on shirt = 25% of market price
∴ Discount = $\frac{25}{100} \times 60$
∴ Discount = $\frac{1}{4} \times 60$
= $\frac{60}{4}$
= $15
SP of shirt = MP - Discount
= 60 - 15
= $45

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

Marked price = $(\frac{100}{100 - Discount%}) \times SP$
= $(\frac{100}{100 - 20}) \times 200$
= $(\frac{100}{80}) \times 200$
= $\frac{20000}{80}$
= $250

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

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 = $\frac{20x}{15}$
Also, SP = $(\frac{100 - Loss%}{100}) \times CP$
Let loss % = y
∴ $\frac{20 x}{15} = (\frac{100 - y}{100}) \times x$
$\frac{20}{15} = (\frac{100 - y}{100})$
15(100 - y) = 20 × 100
1500 - 15y = 2000
- 15y = 2000 - 1500
- 15y = 500
y = $- \frac{500}{15}$
y = $- \frac{100}{3}$
y = $- 33 \frac{1}{3}$
As loss is negative which represents a profit other way around.
∴ there is a profit of $- 33 \frac{1}{3} %$ on one article.

8) A trademark sticks a price label on a 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?

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 = $100 + 100 \times \frac{30}{100}$
= 100 + 30 = $130
Discount offered on marked price of one t-shirt = 20%
Discount = 20% × 130
= $\frac{20}{100} \times 130$
= $26
Selling price of one t-shirt = MP - Discount
= 130 - 26
= $104
Profit = SP - CP
= 104 - 100
= $4
Profit % = $\frac{Profit}{CP} \times 100$
= $\frac{4}{100} \times 100$
= 4%

Fill in Blanks Worksheet

Blanks - 1

The price at which an article is sold is known as its ___.
___ is the price at which an article is purchased.
___ is calculated on the cost price only.
The marked price is also known as ___.
___ are added to the original cost of an article.
The amount deducted from the marked price is called as ___.
___ = selling price - cost price.
Cost price = selling price + ___.
If cost price = 700, selling price = 800, then profit = ___.
If cost price = 700, overhead = 200, then total cost price = ___.

Help box

discount

100

selling price

overhead expenses

900

loss

profit

cost price

listed price

loss percentage

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Write True or False Worksheet

True False - 1

Profit percentage is always calculated on the cost price.
Profit% = $\frac{Profit}{SP} \times 100$
When the selling price of an article is more than its cost price, then it is sold at a profit.
Overhead expenses are not included in the actual cost price.
Discount is given on cost price.
The marked price is called the printed price.
Discount percentage is calculated on the marked price.
Marked price is the sum of selling price and discount.
Loss is calculated as the sum of cost price and selling price.
SP = $(\frac{100 - Discount%}{100}) \times Discount$

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Match Columns Worksheet

Matching - 1

1)	Profit	a)	cost price - selling price
2)	Selling price	b)	marked price - selling price
3)	Loss	c)	selling price - cost price
4)	Discount	d)	marked price - discount
5)	Cost price	e)	selling price + loss

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Solve Questions Worksheet

Solve Questions - 1

Cost price = 300, profit = 10%.
Find profit.
Cost price = 400, loss = 5%.
Find loss.
Cost price = 700, profit = 15%.
Find the selling price.
Cost price = 1000, loss = 10%.
Find the selling price.
Selling price = 1200, loss = 5%.
Find cost price.
Selling price = 1000, profit = 20%.
Find cost price.

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Word Problems Worksheet

Word Problems - 1

A man bought a keyboard for 3200 and sold it for 3000. Find the loss percentage.
A shopkeeper sold the radio whose cost price is 500 at a profit of 10%. Find the selling price of the radio and profit earned by the shopkeeper.
A student bought a book for 100 and sold it further at a loss of 15%. Find the price the student sold it for.
Find profit or loss for:
1. Cost price = 1180, Selling price = 2000
2. Cost price = 2000, Selling price = 1800
Find profit percentage or loss percentage for:
1. Cost price = 1000, Selling price = 1200
2. Cost price = 1500, Selling price = 1700