Profit and Loss Questions

It is crucial to understand the profit and loss question in both academic and practical financial contexts. Determining whether a financial transaction results in a profit or a loss is typically the focus of such

problems. The secret to accurately and rapidly answering such questions is to apply profit and loss problems and utilise the profit and loss formula.

To improve your understanding of profit and loss questions, this thorough guide includes definitions, formulas, examples, and a great deal of practice problems.

 

Table of Contents

• Introduction to Profit and Loss Questions
• Key Terms and Definitions
• Profit and Loss Formula
• Profit and Loss Calculations
• Profit and Loss Problems
• Solved Profit and Loss Examples
• Tips to Solve Profit and Loss Questions
• Practice Word Problems
• Real-Life Applications
• Summary Formula Chart
• Conclusion
• FAQs

 

Introduction to Profit and Loss Questions

Calculating the profit or loss incurred in a transaction is the foundation of profit and loss questions. These questions are especially common in business calculations, competitive exams, and mathematics exams.

Although the formulas are straightforward, accuracy requires close reading and an understanding of the problem.

 

Key Terms and Definitions

To solve profit and loss questions, you must first understand the following key terms:

• Cost Price (CP): The price at which an item is purchased.

• Selling Price (SP): The price at which an item is sold.

• Profit (or Gain): When SP > CP.

• Loss: When CP > SP.

• Profit Percentage: Percentage of profit on CP.

• Loss Percentage: Percentage of loss on CP.

• Marked Price (MP): Labeled price before discount.

• Discount: Reduction on the marked price.

 

Profit and Loss Formula

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

 

 

These profit and loss formulas are used in all types of profit and loss problems related to this topic.

 

Profit and Loss Calculations - Solved Examples

Example 1: Simple Profit

A shirt is bought for ₹400 and sold for ₹480.

Profit = SP – CP = 480 – 400 = ₹80

Profit% = (80 / 400) × 100 = 20%

 

Example 2: Simple Loss

A bag is bought for ₹600 and sold for ₹540.

Loss = 600 – 540 = ₹60

Loss% = (60 / 600) × 100 = 10%

 

Example 3: Find SP with Given Profit%

CP = ₹800, Profit% = 25%

SP = CP × (1 + 25/100) = 800 × 1.25 = ₹1000

 

Example 4: Find SP with Loss%

CP = ₹500, Loss% = 20%

SP = CP × (1 – 20/100) = 500 × 0.8 = ₹400

 

Example 5: Find CP with Given SP and Profit%

SP = ₹1200, Profit% = 20%

CP = SP / (1 + 20/100) = 1200 / 1.2 = ₹1000

 

Example 6: Find CP with SP and Loss%

SP = ₹720, Loss% = 10%

CP = SP / (1 – 10/100) = 720 / 0.9 = ₹800

 

Profit and Loss Problems

Example 1

A person earns a 15% profit on selling a fan for ₹2300. What was the cost price?

CP = SP / (1 + Profit%)

       = 2300 / 1.15

       = ₹2000

 

Example 2

A laptop was sold at a loss of 12% for ₹1760. What is the cost price?

CP = SP / (1 – Loss%)

       = 1760 / 0.88

       = ₹2000

 

Example 3

Question: A pen is bought for ₹40 and sold for ₹50. Find the profit and profit %.

Solution:

C.P. = ₹40, S.P. = ₹50

Profit = 50 – 40 = ₹10

Profit % = (10 / 40) × 100 = 25%

 

Example 4

Question: A book is bought for ₹80 and sold at ₹60. Find the loss and loss %.

Solution:

C.P. = ₹80, S.P. = ₹60

Loss = 80 – 60 = ₹20

Loss % = (20 / 80) × 100 = 25%

 

These profit and loss problems are commonly asked in exams. Using the correct profit and loss formula makes them easy.

 

Solved Profit and Loss Examples

Case 1: Profit Case

Question: A trader buys a mobile phone for ₹7000 and sells it for ₹8400. What is the profit and profit%?

Profit = 8400 – 7000

         = ₹1400

Profit% = (1400 / 7000) × 100

             = 20%

 

Case 2: Loss Case

Question: A fridge is sold for ₹9200 at a loss of 8%. What was the cost price?

CP = SP / (1 – Loss%)

       = 9200 / 0.92

       = ₹10000

 

Case 3: No Profit, No Loss

If SP = CP, then there is neither profit nor loss.

 

Case 4: Discount and Profit

Question: Marked Price = ₹1500, Discount = 10%, Profit% = 20%. Find Cost Price.

Solution:

Selling Price = MP – Discount = 1500 – (10% of 1500) = 1350

Let CP = x

1350 = x × (1 + 20/100)

         = 1.2x
   
x = 1350 / 1.2

   = ₹1125

 

Tips to Solve Profit and Loss Questions

• Always begin by determining CP and SP.

• Don't skip any steps when using simple profit and loss formulas.

• When necessary, convert percentages to decimals.

• Prior to using formulas, determine whether there is a profit or a loss.

• To improve speed, practice various profit and loss problems.
  
  

 

Practice Word Problems

Try solving these profit and loss questions on your own:

Q1. An article was bought for ₹800 and sold for ₹960. Find the profit and profit%.

Q2. A trader bought a camera for ₹5000 and sold it at a 15% loss. What is the SP?

Q3. SP of a table is ₹1320 and CP is ₹1200. Find the profit and profit%.

Q4. A man sold an item for ₹1050 at a 25% loss. What was the cost price?

Q5. A book was sold for ₹450 after making a profit of 20%. What was its cost price?

 

Real-Life Applications

Profit and loss questions apply in:

• Buying and selling of goods

• Business and commerce

• Retail and inventory management

• Budget planning

• Financial investments

• Online/offline marketplaces

Solving profit and loss problems and applying the profit and loss formula can aid smart decisions in both professional and personal finance.

 

Summary Formula Chart

Conclusion

In school math, competitive examinations, and real-world scenarios, profit and loss questions are a crucial topic. These questions can be easily and confidently answered with a thorough understanding of the

profit and loss formula, consistent practice with profit and loss problems, and careful analysis.

To improve your mathematical and financial literacy, keep practicing a range of profit and loss problems and going over actual profit and loss questions.

 

Related Links

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Percentage Questions  - Learn how to calculate percentages easily through practical questions and explanations.

 

FAQs

Q1: What is a profit and a loss?

Answer:

Profit occurs when the Selling Price (S.P.) of an item is greater than its Cost Price (C.P.).

Loss occurs when the Cost Price is greater than the Selling Price.

• Profit = Selling Price – Cost Price

• Loss = Cost Price – Selling Price

 

Q2: What is the formula for profit and loss?

 Answer:

• Profit = Selling Price – Cost Price

• Loss = Cost Price – Selling Price

• Profit % = (Profit / Cost Price) × 100

• Loss % = (Loss / Cost Price) × 100

 

Q3: What does P&L mean?

Answer:

P&L stands for Profit and Loss. It is often used in business to describe a Profit and Loss Statement, which shows whether a company has made a profit or a loss during a specific period.

 

Q4: How to calculate loss of profit?

Answer:

Loss of profit can be calculated using the formula:

Loss of Profit = Expected Profit – Actual Profit

If you know the expected sales price and cost price but the item was not sold, use:

Loss of Profit = Expected Selling Price – Cost Price

 

Q5: How to calculate losses?

Answer:

Use the formula:

Loss = Cost Price – Selling Price

To find the percentage loss:

Loss % = (Loss / Cost Price) × 100

 

Keep practicing profit and loss questions to strengthen your calculation skills. Explore more math concepts with Orchids The International School!