Profit and Loss in mathematics is a very crucial concept to learn as it is used in our real life. All businesses and financial institutes calculate their worth of work depending on the profit and loss they gained every year. We will also see different concepts while learning about profit and loss. You can also read about the cost price, selling price, discount, marked price, etc. By understanding the complete profit and loss concepts, you can easily estimate how a business is running with its success rate.

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## Important Concepts of Profit and Loss

Let us deeply discuss the main concepts of profit and loss. The other related terms like cost price and selling price are also explained in detail here.

### Profit (P)

In simple words, if you sell any product with more amount than you buy it, then you will get a profit amount. The Profit represents by the letter P.

#### Profit Formula

(i) If the cost price of a product or item and the selling price of a product or item is given, then the profit can be calculated by subtracting the cost price from the selling price. That is

Profit = Selling Price (S. P) – Cost Price (C. P.)

(ii) If the Revenue is given along with the Cost of Goods Sold, then the Gross Profit can be calculated by subtracting the Cost of Goods Sold from the Revenue. That is

Gross Profit = Revenue – Cost of Goods Sold

#### Examples on Profit

**Example 1.** A merchant bought 30 dresses, each at a price of Rs 150. He sold each of them for Rs. 200. Find his profit on the dresses?

**Solution:** Given that a merchant bought 30 dresses, each at a price of Rs 150.

Cost Price = Rs 150

He sold each of them for Rs. 200

Selling Price = Rs. 200

Profit = Selling Price (S. P) – Cost Price (C. P.)

Substitute the Cost Price and Selling Price on the above formula.

Profit = Rs. 200 – Rs. 150

Profit = Rs. 50

He got a profit of Rs. 50 on each dress.

For 30 dresses, Rs. 50 × 30 = Rs. 1500.

Therefore, the total profit he gained on the 30 dresses is Rs. 1500

**Example 2.** A book was bought at a price of Rs 50 and sold at a cost of Rs. 100. Find the profit on the book?

**Solution:** Given that a book was bought at a price of Rs 50 and sold at a cost of Rs. 100.

Cost Price = Rs 50

The book sold at a price of Rs. 100

Selling Price = Rs. 100

Profit = Selling Price (S. P) – Cost Price (C. P.)

Substitute the Cost Price and Selling Price on the above formula.

Profit = Rs. 100 – Rs. 50

Profit = Rs. 50

Therefore, the profit gained from the book is Rs. 50.

### Loss (L)

The loss amount is the amount occurred when you sell any product with less amount than you buy it. The Loss represents by the letter L.

#### Loss Formula

(i) If the cost price of a product or item and the selling price of a product or item is given, then the loss can be calculated by subtracting the selling price from the cost price. That is

Loss = Cost Price (C. P.) – Selling Price (S. P)

#### Examples on Loss

**Example 1.** A shop owner buys a product for $40. He sells that product for $30 each. Using the loss formula, calculate the loss obtained on that product?

**Solution:** Given that the shop owner buys a product for $40. He sells that product for $30 each.

The cost price of the product = $40.

He sells that product for $30 each.

The selling price of the product = $30.

Loss = Cost Price (C. P.) – Selling Price (S. P)

Substitute the Cost Price and Selling Price on the above formula.

Loss = $40 – $30 = $10.

Therefore, the loss obtained on that product is $10.

**Example 2.** John bought a wallet for $500 and on selling that wallet at a price of $300 he faced a loss. How much loss he faced on selling a wallet.

**Solution:** Given that John bought a wallet for $500 and on selling that wallet at a price of $300 he faced a loss

The cost price of the wallet = $500

Selling Price of the wallet = $ 300.

Now, find the loss obtained on the wallet.

Loss = Cost Price – Selling Price

Substitute the Cost Price and Selling Price on the above formula.

Loss = $500 – $300 = $200.

Therefore, the loss obtained on selling his wallet is $200.

### Profit Percentage

We can calculate the profit percentage by knowing the profit and cost price. The formula to find the profit percentage is

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

Profit Margin = (Total Income/Net Sales) × 100

Gross Profit Margin = (Gross Profit/Net Sales) × 100

#### Examples of Profit Percentage

**Example 1.** A shopkeeper buys biscuits in bulk for Rs. 15 each. He sold them for Rs. 35 each. Calculate the profit and the profit percentage.

**Solution:** Given that a shopkeeper buys biscuits in bulk for Rs. 15 each.

Cost Price = Rs 15

He sold each of them for Rs. 35 each.

Selling Price = Rs. 35

Profit = Selling Price (S. P) – Cost Price (C. P.)

Substitute the Cost Price and Selling Price on the above formula.

Profit = Rs. 35 – Rs. 15

Profit = Rs. 20

He got a profit of Rs. 20

Profit% = (Profit / C.P.) × 100

Profit% = (Rs.20 / Rs.15) × 100

Therefore, the total profit% he gained on the biscuits is Rs. 133%

**Example 2.** Raj bought a car for Rs. 100000 and he sold it for Rs.150000. Is it the condition of profit or loss? Also, find the profit or loss percentage incurred by him.

**Solution:** Given that Raj bought a car for Rs. 100000 and he sold it for Rs.150000.

Cost price (CP) of the bike = Rs. 100000

Selling price (SP) of the bike = Rs.150000

As the Cost price (CP) is less than the Selling price (SP), it is a profit.

Profit = Selling Price (S. P) – Cost Price (C. P.)

Substitute the Cost Price and Selling Price on the above formula.

Profit = Rs.150000 – Rs. 100000 = Rs. 50000

Now, find the profit%

Profit% = (Profit / C.P.) × 100

Substitute the profit and Cost Price in the above formula.

Profit% = (Rs. 50000 / Rs. 100000) × 100 = 50%

Therefore, the profit% is 50%.

### Loss Percentage

We can calculate the Loss percentage by knowing the loss and cost price. The formula to find the loss percentage is

Loss Percentage = (Loss × 100)/C. P

#### Examples of Loss Percentage

**Example 1.** A shopkeeper buys a TV at a price of Rs. 35000. He sold it for Rs. 30000. Calculate the loss and the loss percentage.

**Solution:** Given that a shopkeeper buys a TV at a price of Rs. 35000.

Cost Price = Rs 35000

He sold it at a cost of Rs. 30000.

Selling Price = Rs. 30000

Loss = Cost Price (C. P.) – Selling Price (S. P)

Substitute the Cost Price and Selling Price on the above formula.

Loss = Rs. 35000 – Rs. 30000

Loss = Rs. 5000

He got a loss of Rs. 5000

Loss% = (Loss × 100)/C. P

Loss% = (Rs.5000 × 100)/Rs.35000

Therefore, the Loss% obtained on selling a TV is 14.28%

**Example 2.** Find the loss and loss percentage provided that the cost price is Rs. 60 and the selling price is Rs. 50.

**Solution: **Given that the cost price is Rs. 60 and the selling price is Rs. 50.

Cost Price = Rs. 60

Selling Price = Rs. 50.

Loss = Cost Price (C. P.) – Selling Price (S. P)

Substitute the Cost Price and Selling Price on the above formula.

Loss = Rs. 60 – Rs. 30000

Loss = Rs. 5000

He got a loss of Rs. 5000

Loss% = (Loss × 100)/C. P

Loss% = (Rs.5000 × 100)/Rs.35000

Therefore, the Loss% obtained on selling a TV is 14.28%

#### Important Formulas of Profit and Loss

Check out the below formula to know how to calculate profit and loss. You can completely understand the concept of profit and loss with the help of these below tricks. Therefore, note down all the formulas and remember every formula to solve problems easily.

(i) Profit (P) = Selling Price (SP) – Cost Price (CP) when SP > CP.

(ii) Loss (L) = Cost Price (CP) – Selling Price (SP) when CP > SP.

(iii) Profit Percentage (P%) = (Profit/Cost Price) x 100

(iv) Loss Percentage (L%) = (Loss/Cost Price) x 100

(v) Selling Price (SP) = {(100 + P%)/100} x Cost Price (CP)

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

(vii) Cost Price (CP) = {100/(100 + P%)} x Selling Price (SP)

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

(ix) Discount = Marked Price (MP) – Selling Price (SP)

(x) Selling Price (SP) = Marked Price (MP) – Discount

(xi) If Profit percentage P% and loss percentage L% are equal then, P = L and %loss = P^2/100.

(xii) If the profit is x% and loss is y%, then the net % profit or loss will be: (x-y-xy)/100

(xiii) If there are two successful profits say x% and y%, then the net percentage profit equals (x+y+xy)/100

(xiv) For false weight, profit percentage P% = (True weight – false weight/ false weight) x 100.

(xv) If a product or item 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 P/(100-x)(100-y)]

### FAQs on Profit and Loss

**1. What are Profit and Loss?**

Profit can be calculated by doing Selling Price (S. P) – Cost Price (C. P.).

Loss can be calculated by doing Cost Price (C. P.) – Selling Price (S. P).

**2. How To Calculate Profit and Loss Percentage?**

To Calculate Profit and Loss Percentages, we must know the selling price and cost price of the product. The main formula to calculate the profit and loss are

Profit = Selling Price – Cost Price

Loss = Cost Price – Selling Price

The formulas that are used to calculate the profit and loss percentage are

Profit percentage (P%) = (Profit /Cost Price) × 100

Loss percentage (L%) = (Loss / Cost price) × 100

**3. If a shopkeeper has bought 1 kg of grapes for 50 rs. And sold it for Rs. 100 per kg. How much is the profit gained by him?**

Profit = selling price – cost price

Profit = 100 – 50 = 50

The profit is 50 rupees.

**4. How to calculate the profit when Profit percentage and Cost Price are given?**

P = (P% x 100)/CP where p is the profit, P% is the Profit percentage, and CP is the Cost Price.

**5. What is the discount?**

It is the deduction in the actual price of a product.