Profit and Loss: Formula, Questions, Solved Examples & Practice

Profit and loss helps us understand whether we earn money or lose money when buying and selling products. By comparing the cost price (CP) and selling price (SP), we can calculate the profit, loss, and their percentages. These concepts are widely used in shopping, business, and everyday financial decisions.

In this article, you'll learn the meaning of profit and loss, important terms, formulas, methods to calculate cost price and selling price, solved examples, practice questions, and real-life applications in a simple and easy-to-understand way.

Table of Contents

• What is Profit and Loss?
• Basic Terms You Need to Know
• Profit and Loss Formulas
• How to Calculate the Selling Price of a Product?
• How to Calculate the Cost Price of a Product?
• Solved Examples of Profit and Loss
• Profit and Loss Practice Questions
• Real-Life Applications of Profit and Loss
• Common Misconceptions
• Frequently Asked Questions on Profit and Loss

What is Profit and Loss?

Profit and Loss is the branch of arithmetic that compares the Cost Price (CP)- what you paid for something with the Selling Price (SP) - what you sold it for.

• If SP > CP → Profit = SP − CP
• If CP > SP → Loss = CP − SP

Profit or loss is always expressed as a percentage of the Cost Price, never the selling price.

Basic Terms You Need to Know

Profit:

Profit is the money made by an individual or company when they sell something for a price higher than its cost price or its creation cost. In simple words, profit occurs when the price of selling is higher than the cost price.

Loss:

Loss is the quantity of money that an individual or company loses when they sell a product or thing for lower than what they paid or created it for. That is, loss occurs when the cost price is greater than the selling price.

Cost Price

Cost price abbreviated as C.P, is the basic price of an article.

It is the price paid to purchase or produce a product in order to sell it.

In other words:

Cost Price is the money you pay to acquire something.

• It is the initial amount at which a product is offered.

• It may involve the cost of purchase, shipping, duty, and other expenses incurred to prepare the item for sale.

• It is employed in determining Profit or Loss upon selling the item.

Selling Price

Selling Price, abbreviated as S.P., is the price given when a commodity is sold to an individual.

In simple terms:

Selling Price is money you receive when selling something.

• It is the last price at which a good is sold.

• It can be equal to, greater than, or lesser than the Cost Price.

• It assists us in determining if we earned a profit or a loss.

Marked Price

Marked Price, abbreviated as M.P, is the price marked on the label or tag of an item prior to providing a discount.

In simple terms:

Marked Price is the price indicated on the product, normally prior to offering a discount.

• It is also referred to as the List Price or Label Price.

• This is the price fixed by the shopkeeper or seller.

• The Selling Price can actually be lower than the Marked Price in case of a discount.

Discount

The amount which is offered by the seller to reduce the selling price is called the discount.

While selling a product three conditions may arise:

1. Cost Price is less than selling price, i.e., C.P < S.P

2. Cost price is more than the selling price, i.e., C.P > S.P

3. Cost price is equal to the selling price, i.e., C.P = S.P.

Based on this condition the seller either makes a profit or a loss.

Profit and Loss Formulas

Here are the core profit and loss formulas used to solve most questions:

Solved Example Of Profit and Loss

Practice different types of profit and loss questions to understand how profits, losses, and percentages work in math as well as in real life.

Example 1: The cost price of an article is ₹74 and the selling price is ₹86 each. Find the profit made in selling 23 such articles.

Solution:

Step 1: The cost price of an article is ₹74.

Multiply 74 by 23 to get the cost price of 23 articles.

74 × 23 = 1,702

Step 2: The selling price of an article is ₹86.

Multiply 86 by 23 to get the selling price of 23 articles.

86 × 23 = 1,978

Step 3: Subtract 1,702 from 1,978 to get the profit.

Profit = Selling Price - Cost price 

= 1,978 - 1,702 = 276

Therefore, the profit made in selling 23 articles is ₹276.

Example 2: Bhavan bought 20 boxes of gifts for ₹1,642. He sold each box for ₹58. Find the loss or profit made by him.

Solution:

Step 1: The selling price of 1 box = ₹58.

Number of boxes = 20

Total selling price = 58 × 20 = 1,160

Step 2: The cost price of 20 boxes = ₹1,642.

The selling price of 20 boxes = ₹1,160

Loss = Cost Price - Selling Price

Loss = 1,642 - 1,160 = 482

Example 3: During a festive sale, a store offers two successive discounts of 10% and 15% on a jacket marked at ₹4,000. Find the final selling price and the single equivalent discount percentage.

Solution:

MP = ₹4,000

After 1st discount (10%): 4,000 × 90/100 = ₹3,600

After 2nd discount (15%): 3,600 × 85/100 = ₹3,060

Final SP = ₹3,060

Total discount given = 4,000 − 3,060 = ₹940

Equivalent single discount% = (940 ÷ 4,000) × 100 = 23.5%

Two successive discounts of 10% and 15% are NOT the same as a flat 25% discount; the equivalent is 23.5%.

Example 4: A dishonest grocer uses a weight of 900 g instead of 1 kg while buying and selling goods at the cost price itself. Find his profit percentage.

Solution:

He claims to give 1000 g but actually gives only 900 g.

Gain = Error = 1000 − 900 = 100 g

Profit% = (Error ÷ True Value) × 100 = (100 ÷ 900) × 100

Profit% = 11.11% (approximately)

Even while 'selling at cost price,' the grocer earns a hidden profit of 11.11% through the faulty weight.

Example 5: A trader bought 80 kg of rice for ₹3,200. He sold 50 kg at a profit of 10% and the remaining 30 kg at a loss of 5%. Find his overall profit or loss percentage.

Solution:

CP per kg = 3,200 ÷ 80 = ₹40

CP of 50 kg = 50 × 40 = ₹2,000; sold at 10% profit

⇒ SP = 2,000 × 110/100 = ₹2,200

CP of 30 kg = 30 × 40 = ₹1,200; sold at 5% loss

⇒ SP = 1,200 × 95/100 = ₹1,140

Total SP = 2,200 + 1,140 = ₹3,340

Total CP = ₹3,200; Overall Profit = 3,340 − 3,200 = ₹140

Overall Profit% = (140 ÷ 3,200) × 100 = 4.375%

The trader makes an overall profit of 4.375%, even though part of the rice was sold at a loss. 

Profit and Loss Practice Questions

1. A bag was sold for ₹900 with a profit of ₹100. Find the profit percentage.

2. A laptop was sold for ₹18,000 at a loss of ₹2,000. What is the loss percentage?

3. Selling Price = ₹750, Profit = ₹150. Find the Cost Price.

4. Cost Price = ₹1,000, Profit % = 25%. What is the Selling Price?

5. Meena bought 15 storybooks for ₹90 each and sold them all for ₹100 each. What is her total profit?

6. A shopkeeper sold a fan for ₹2,400 after giving a discount of ₹600. What was the marked price of the fan?
   
   

Real-Life Applications of Profit and Loss

Profit and loss are used in many everyday situations to help people make smart financial decisions. Here are a few real-life examples where understanding profit and loss is useful:

• Retail and kirana stores: Every shopkeeper marks goods above cost price specifically to absorb the discounts they plan to offer during festive sales while still protecting their margin.
• Online shopping: When an e-commerce site shows 'MRP ₹1,999, you pay ₹1,299,' it's directly using the MP − Discount = SP formula you just learned.
• Stock market investing: Buying shares at one price and selling at another is profit and loss at a larger scale, the percentage calculation is identical.
• Household budgeting: Comparing prices at the local market versus the supermarket, or deciding whether a "buy 1 get 1" offer is genuinely a good deal, uses the exact same percentage logic.

Common Misconceptions

1: Profit is always a good thing, and loss is always bad.

Reality: While profit usually means earning more money, it’s not always good if it involves cheating or overpricing. Similarly, a loss isn’t always bad—sometimes items are sold at a loss to clear old stock or attract more customers.

2: Profit = Selling Price - Marked Price

Reality: Profit is calculated as Profit = Selling Price - Cost Price, not the marked price. The marked price is often higher and only used to calculate discounts, not profit or loss.

3: If there is a discount, the seller always faces a loss.

Reality: Giving a discount does not always result in a loss. If the discounted selling price is still higher than the cost price, the seller still makes a profit.

4: Loss means losing all the money spent.

Reality: A loss means that the selling price is less than the cost price, but it doesn’t mean the entire amount is lost. It’s just the difference between cost price and selling price.

5: Profit or loss is always calculated on the selling price.

Reality: Profit and loss percentages are always calculated based on the cost price, not the selling price.
Example: Profit % = (Profit ÷ Cost Price) × 100

 

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