Profit and Loss are concepts in mathematics that help us determine that the market price of a commodity is sold for a price more than the price at which the commodity is bought or less the price. In mathematics, the profit and loss concept is used to determine the market price of a good and whether or not it is profitable. Every product on the market has a cost price as well as a selling price. Knowing the cost and selling prices of a commodity allows you to calculate the acquired profit or loss.

For example, a businessman makes a profit when the selling price of an item is higher than the cost price of that item, and a loss when the cost of purchasing the item is more than the selling price. This article explores all the concepts related to Profit and Loss, whether it’s their formula or their percentage formula. Here we will also learn about the marked up price as well as discount.

Basic Concepts of Profit and Loss

In Profit and Loss, the most basic concepts are the prices of various items throughout the cycle of their purchase and sale. These prices are Cost Price, Selling Price, and Marked Price which are abbreviated as C.P., S.P., and M.P., respectively. Let’s understand these concepts in detail as follows:

Cost Price (CP)

The cost price (CP) of a product is the amount paid for it. In some cases, it also covers overhead costs, transportation costs, etc.

For example: You bought a refrigerator at Rs 20,000 and spent Rs 4000 for transportation and Rs 1000 for set up. So the total cost price is the sum of all the expenditures done which will be Rs 25000.

Cost Price Formula

The formula for cost price is given as

Cost Price = Selling Price – Profit

Cost Price = Selling Price + Loss

Let’s consider an example for better understanding.

Example: Sarah sold here bicycle for Rs. 5000 while making a profit of Rs. 570. Then what is the price at which she bought that cycle.

Answer:

Given: Selling Price (SP) = Rs. 5000, and

Profit = Rs. 570

Thus, Cost Price = Selling Price – Profit

⇒ Cost Price = 5000 – 570

⇒ Cost Price = 4430.

Thus, the cost price of the bicycle is Rs. 4430.

Selling Price (SP)

The selling price (SP) of a product is the amount at which it is sold. It might be greater, equal to, or less than the product’s cost price.

For example: If a shopkeeper bought a chair at Rs 1500 and sold it at Rs 1900, then the cost price of the chair is Rs 1500 and the selling price of the chair is Rs 1900.

Selling Price Formula

The formula for cost price is given as

Selling Price = Cost Price + Profit

Selling Price = Cost Price – Loss

Let’s consider an example for better understanding of the formula.

Example: John bought a mobile phone for Rs. 8000 and then sold it at a loss of Rs. 1200. What was the selling price of the mobile phone?

Answer:

Given: Cost Price (CP) = Rs. 8000, and

Loss = Rs. 1200

Using the formula:

Selling Price (SP) = Cost Price – Loss

⇒ Selling Price (SP) = Rs. 8000 – Rs. 1200

⇒ Selling Price (SP) = Rs. 6800

Therefore, the selling price of the mobile phone is Rs. 6800.

Marked Price (MP)

It is the price that is displayed on an item or commodity. It is sometimes referred to as the list price or the tag price. If there is no discount applied to the listed price, the selling price is the same as the marked price.

For example: Suresh goes to a mall for shopping where every product is given a discount offer of 60%. When the price on a stand is written as Rs.150. It implies that the Marked Price of the stand before the discount is Rs. 150.

Marked Price Formula

The formula for Marked price is given as

Marked Price = Selling Price + Discount

For better understanding for use of formula let’s consider the following example.

Example: Emily purchased a watch for Rs. 1500 after getting a discount of Rs. 300 on the marked price. What was the marked price of the watch?

Answer:

Given: Selling Price (SP) = Rs. 1500, and

Discount = Rs. 300

Using the formula:

Marked Price (MP) = Selling Price + Discount

⇒ Marked Price (MP) = Rs. 1500 + Rs. 300

⇒ Marked Price (MP) = Rs. 1800

Therefore, the marked price of the watch was Rs. 1800.

What are Profit and Loss?

Profit and Loss are two major financial concepts which help us understand vast variety of things from daily budgeting to complex economical models. Profit and Loss also help us estimate the market price of a commodity and to assess how profitable a firm is. There is a selling price and a cost price for every product. Based on the values of these prices, we may compute the profit or loss for a certain product.

Profit (P)

Profit is defined as the amount gained by selling a product that is more than the product’s cost price. It is the total amount gained from any business activity.

For example: If a plot was purchased at Rs 150,000 and three years later it was sold at Rs 3,50,000 then there is a profit of 2 lakh.

Loss (L)

When a product is sold for less than its cost price, the seller incurs a loss.

For example: If an I-pad is bought at Rs 30,000 and a year later it was sold for Rs 20,000 then the seller made a loss of Rs 10000.

Profit and Loss Formula

Different formulas for Profit and Loss are discussed in the following:

Profit Formula

Profit is better defined as the difference between the cost price and the selling price. A product’s or commodity’s cost price is its real price, but the selling price is the amount at which the product or commodity is sold. So, if the product’s selling price surpasses its cost price, the corporation has generated a profit.

Profit = S.P. – C.P.

Where,

• C.P. is the cost price of the goods, and
• S.P. is the selling price of the goods.

Loss Formula

When the cost price of a transaction is greater than the selling price, we incur a loss.

For Example: If a salesperson has bought a textile material for Rs.500 and has to sell it for Rs.350/-, he has incurred a loss of Rs.150/-.

Loss = C.P. – S.P.

Where,

• C.P. is the cost price of the goods, and
• S.P. is the selling price of the goods.

Discount Formula

When the item is sold at a price which is less then the marked price, then we say item is sold at discount and it can be calculated using the formula,

Discount  = M.P. – S.P.

Where,

• M.P. is the marked price of the goods, and
• S.P. is the selling price of the goods.

Profit and Loss Percentage Formula

Profit and Loss percentage is the profit and loss represented in the form of percentage and the formula for these are discussed as follows:

Profit Percentage

Profit percentage (%) represents the amount of profit as a percentage of the total. Because this profit is proportional to the cost price, the profit Percentage Formula is based on Profit and C.P.

As a result of this, The profit calculation formula will be:

Profit Percent = (Profit × 100)/ C.P. 

Where C.P. is the cost price of the goods.

Loss Percentage

The loss percentage formula is used to compute the percentage loss in any parameter and as we already know that the difference between the cost price and the selling price is known as the loss. And the percentage loss is the loss as a percentage of the actual cost price.

Loss Percentage = (Loss x 100)/C.P

Where C.P. is the cost price of the goods.

Discount Percentage

Discount Percentage is the discount represented in the percentage form and can be calculated using the following formula:

Discount Percentage = (Discount / M.P.) × 100

Where M.P. is the marked price of the goods.

Profit and Loss Tricks

There are various points or short tricks that can be remembered to solve the problems of Profit and Loss with ease. Some of such points are as follows:

• Profit (P) = SP – CP If SP > CP
• Loss (L) = CP – SP If CP > SP
• Profit (P%) = (P/CP) x 100
• Loss (L%) = (L/CP) x 100
• Selling Price (SP) = {(100 + P%)/100} x CP
• Selling Price (SP) = {(100 – L%)/100} x CP
• Cost Price (CP) = {100/(100 + P%)} x SP
• Cost Price (CP) = {100/(100 – L%)} x SP
• Discount = Marked Price – Selling Price
• Selling Price = Marked Price – Discount
• When there are two profits, say x% and y%, then the net percentage of profit equals to [x+y+(xy/100)]
• When the profit is x%, and loss is y%, then the net % of profit or loss will be: [x-y-(xy/100)]
• If a product is sold at x% profit and then again sold at y% profit then the actual cost price of the product will be CP = [100 x 100 x P/(100+x)(100+y)]. In case of loss, CP = [100 x 100 x L/(100-x)(100-y)]
• If Profit % and Loss % are equal then, P = L and %loss = (Profit)2/100

How to Calculate Profit and Loss?

The cost price and selling price of the goods must be known in order to compute profit and loss. We can use the following steps to calculate the profit and loss for any given data set.

Step 1: Check whether the cost price is greater than the selling price or the selling price is greater than the cost price.

Step 2: If the cost price is greater than the selling price, then calculate the Loss using the following formula:

Loss = Cost Price – Selling Price

Step 3: If the Selling Price is greater than the cost price, then calculate the profit using the following formula:

Profit = Selling Price – Cost Price

Profit and Loss Examples

Example 1: A shopkeeper buys pens in bulk for Rs. 30 each. He sells each of them for Rs. 65. What will be the profit and the profit percentage?

Solution: 

Given: Selling price of the Pen (S.P) = Rs. 65

Cost price of the Pen (C.P) = Rs. 30

Now, As per the profit formula,

Profit = Selling Price – Cost Price

So, profit = 65 – 30 

Profit = Rs. 35

Now, Using the formula for profit percentage,

Profit % = (Profit / Cost Price ) × 100

So, the profit percentage = (35 / 30) × 100 

= 1.16 × 100 

Profit percentage = 116%.

Example 2: If a vendor sells fruits at Rs.350 per kg, whose cost price is Rs.250/- per kg. What will be the profit gained by the vendor? Find the profit percentage.

Solution:

Given, Cost Price = Rs.250/-

Selling Price = Rs.350/-

As we know, Profit formula

Profit = Selling Price – Cost Price

Profit = 350 – 250

Profit = 100

Therefore, the vendor earn profit Rs. 100/-

Now, To calculate Profit Percentage

Profit % = (Profit / Cost Price ) × 100

= (100 /250) x 100

Example 3: Ankit bought a plot at Rs 3,27,000. He wanted an overall profit of 14% but he sold one-third of the plot at a loss of 6% so at what price should he sell the remaining plot of land? 

Solution:

The cost price of the entire plot = Rs 3,27,000. 

  Cost price of 1/3rd of the plot = 1/3 x 3,27,000

= Rs109000

Loss Percentage = (Loss x 100)/C.P

6 = (loss x 100)/ 109000

loss = (6 x 109000)/100

= 6540

Ankit suffered a loss of Rs 6540 on selling 1/3rd of the land 

SP for 1/3rd of the land = 109000 – 6540 = 102460

To make a profit of 14% of 3,27,000, is

 P% = (Profit / Cost Price ) × 100

14 = (profit / 327000) x 100

profit = (14 x 327000)/100

= Rs 45780

Thus, to get a profit of Rs 45780

SP = 3,27,000 + 45780 = Rs 3,72,780

Ankit has already sold 1/3rd of the land at Rs 102460 thus he needs to sell the remaining land at Rs (3,72780 – 102460) = Rs 270320.

Therefore, Ankit needs to sell the remaining plot at Rs 270320.

Example 4: A man buys a cooler for Rs. 10000 and sells it at a loss of 14%. What is the selling price of the cooler?

Solution:

Cost Price of the cooler is Rs.10000

Loss percentage is 14%

As we know, Loss percentage = (Loss/Cost Price) x 100

14 = (Loss/10000) x 100

Loss = (14 x 10000)/100

= 1400

Loss = Cost Price – Selling Price

So, Selling Price = Cost Price – Loss

= 10000 – 1400

Selling Price = Rs 8600

The selling price of the cooler is Rs 8600

Example 5: A shopkeeper buys juice cans in bulk for Rs 50 each. He sells them for Rs 30 each. Calculate the loss and the loss percentage.

Solution:

To find: Loss and Loss Percentage

Given : Selling price = Rs 30 and Cost price = Rs 50

Using loss formula,

Loss = C.P. – S.P.

Loss = 50 – 30

= Rs 20

Using Loss Percentage Formula,

Loss% = (loss/ C.P.) × 100

Loss Percentage = (20 /50) × 100

Answer: Loss = Rs 20 and loss percentage = 40%.

Practise Problems on Profit and Loss

Some practise problems based on the topics discussed on the topic of Profit and Loss, are:

Problem 1: A shopkeeper bought a shirt for ₹300 and sold it for ₹500. Calculate the profit percentage he made on the shirt.

Problem 2: A company bought a machine for ₹10,000. They spent an additional ₹2,000 on its maintenance and repairs. If they sold the machine for ₹15,000, what is the profit or loss percentage?

Problem 3: A bookstore bought 100 books at ₹110 each. The bookstore sold 80 books at ₹320 each and the rest were sold at a discount of 50% due to some damage. Calculate the overall profit or loss percentage for the bookstore.

Problem 4: Sara bought a bicycle for ₹4000 and later sold it to her friend at a loss of 20%. Her friend then sold it to another person for ₹3000. What was the percentage profit or loss for Sara’s friend?

Problem 5: John bought a used laptop for ₹15000 and spent ₹2000 on repairs. He then sold the laptop for ₹22000. Calculate the profit or loss percentage for John.

FAQs on Profit and Loss

1. What is the difference between the cost price and the selling price?

The cost price of a product is the price at which it is purchased, and the selling price is the price at which it is sold.

2. What is the Profit Formula?

Profit = Selling Price – Cost Price, is the formula used to compute profit in a transaction.

3. What is the formula for discount?

A discount is the reduction provided by a merchant on a marked price.

The following formula is used to calculate the discount in terms of SP and MP: Discount = Marked Price – Selling Price.

4. What is the formula for the selling price?

It generally refers to the price at which an item is sold. If the vendor makes a profit, then

 S.P. = C.P. + Profit.

5. How to calculate the CP?

The cost price (CP) of a product is the amount paid for it. In some cases, it also covers overhead costs, transportation costs, etc Cost Price (CP) = {100/(100 + P%)} x SP

Cost Price (CP) = {100/(100 – L%)} x SP