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 Questions with Solutions
• Tips to Solve Profit and Loss Questions
• Practice Word Problems
• Real-Life Applications
• Summary Formula Chart
• Conclusion
• FAQs On Profit and Loss Questions

 

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): Labelled 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 Questions with Solutions

Question 1: 

A shirt is bought for ₹400 and sold for ₹480. Find the profit and profit%.

Solution:
C.P. = ₹400
S.P. = ₹480

Profit = S.P. - C.P. = 480 - 400 = ₹80

Profit% = (Profit / C.P.) × 100
= (80 / 400) × 100 = 20%

 

Question 2: 

A bag is bought for ₹600 and sold for ₹540. Find the loss and loss%.

Solution:
C.P. = ₹600
S.P. = ₹540

Loss = C.P. - S.P. = 600 - 540 = ₹60

Loss% = (Loss / C.P.) × 100
= (60 / 600) × 100 = 10%

 

Question 3: 

The cost price of a table is ₹800. If the profit% is 25%, find the selling price.

Solution:
C.P. = ₹800
Profit% = 25%

S.P. = C.P. × (1 + Profit%/100)
= 800 × (1 + 25/100)
= 800 × 1.25
= ₹1000

 

Question 4: 

The cost price of a chair is ₹500. If the loss% is 20%, find the selling price.

Solution:
C.P. = ₹500
Loss% = 20%

S.P. = C.P. × (1 - Loss%/100)
= 500 × (1 - 20/100)
= 500 × 0.8
= ₹400

 

Question 5: 

A fan is sold for ₹1200 at a profit of 20%. Find the cost price.

Solution:
S.P. = ₹1200
Profit% = 20%

C.P. = S.P. / (1 + Profit%/100)
= 1200 / 1.2
= ₹1000

 

Question 6: 

A TV is sold for ₹720 at a loss of 10%. Find the cost price.

Solution:
S.P. = ₹720
Loss% = 10%

C.P. = S.P. / (1 - Loss%/100)
= 720 / 0.9
= ₹800

 

Question 7: 

The marked price of an article is ₹1500. A discount of 10% is given, but still the shopkeeper makes a profit of 20%. Find the cost price.

Solution:
Marked Price (M.P.) = ₹1500
Discount = 10%

S.P. = M.P. - (10% of 1500) = 1500 - 150 = ₹1350

Let C.P. = x

Now, S.P. = C.P. × (1 + Profit%/100)
1350 = x × 1.2

x = 1350 / 1.2 = ₹1125

 

Question 8: 

A trader buys an article for ₹500. He first gains 20% and then sells it at a loss of 10%. Find the final selling price and overall profit/loss%.

Solution:
Step 1: First transaction → Profit = 20%
S.P. = 500 × (1 + 20/100) = 500 × 1.2 = ₹600

Step 2: Second transaction → Loss = 10%
Final S.P. = 600 × (1 - 10/100) = 600 × 0.9 = ₹540

Now,
C.P. = ₹500, Final S.P. = ₹540

Profit = 540 - 500 = ₹40
Profit% = (40 / 500) × 100 = 8% Profit

 

Question 9: Same S.P. with Gain and Loss

A man sells two articles at the same selling price. On one he gains 20% and on the other he loses 20%. What is the overall result?

Solution:
Shortcut Formula:
Overall Loss% = (Common Gain% × Common Loss%) / 100

= (20 × 20) / 100 = 4% Loss

 

Question 10: 

A shopkeeper marks an article 40% above its cost price and allows a discount of 10%. Find his profit percentage.

Solution:
Let C.P. = ₹100

Then M.P. = 100 × (1 + 40/100) = ₹140

S.P. = 140 - (10% of 140) = 140 - 14 = ₹126

Profit = 126 - 100 = ₹26

Profit% = (26 / 100) × 100 = 26%

Question 11:

A trader buys 60 identical items for ₹4,800. He sells 20 items at 10% profit, 20 items at 10% loss and the remaining at cost price. What is his overall profit or loss %?

Solution:

Total C.P. = ₹4,800
C.P. of one item = 4800/60 = ₹80

First 20 items:
C.P. = 20 × 80 = ₹1600
S.P. at 10% profit = 1600 × 1.10 = ₹1760

Next 20 items:
C.P. = ₹1600
S.P. at 10% loss = 1600 × 0.90 = ₹1440

Remaining 20 items sold at cost:
S.P. = C.P. = ₹1600

Total S.P. = 1760 + 1440 + 1600 = ₹4800

Total C.P. = ₹4800

Net result = No profit, no loss → 0%

 

Question 12:

A man buys a bicycle for ₹3,200 and spends ₹300 on repairs. He sells the bicycle for ₹3,650. Find his profit %.

Solution:

C.P. = 3200 + 300 = ₹3500

S.P. = ₹3650

Profit = 3650 – 3500 = ₹150

Profit% = (150 / 3500) × 100 = (150 × 100)/3500 = 15000/3500 = 15/3.5 = 4.2857% ≈ 4.29%

 

Question 13:

A merchant sells two articles for ₹2,000 each. On one he gains 25% and on the other he loses 25%. Calculate his overall profit or loss %.

Solution:

Let C.P. of first article = x
S.P. of first = 2000 = x × (1 + 25/100) = 1.25x → x = 2000 / 1.25 = ₹1600

Let C.P. of second = y
S.P. of second = 2000 = y × (1 – 25/100) = 0.75y → y = 2000 / 0.75 = ₹2666.6667

Total C.P. = 1600 + 2666.6667 = ₹4266.6667
Total S.P. = 2000 + 2000 = ₹4000

Loss = Total C.P. – Total S.P. = 4266.6667 – 4000 = ₹266.6667

Loss% = (266.6667 / 4266.6667) × 100 = (266 2/3 ÷ 4266 2/3) ×100 = (0.0625) ×100 = 6.25% Loss

(Exact calculation: C.P.s are 1600 and 8000/3 → total = (4800+8000)/3 = 12800/3; loss = (12800/3 – 4000) = (12800 – 12000)/3 = 800/3; loss% = (800/3) / (12800/3) ×100 = 800/12800 ×100 = 1/16 ×100 = 6.25%)

 

Question 14:

A retailer buys an article for ₹420. He intends to earn 25% profit, but gives a discount of 10% on the marked price. At what percentage above cost should he mark the article so that after discount he gets the desired 25% profit?

Solution:

Let required markup percentage = m%.
Let C.P. = ₹420.

He wants final S.P. = 420 × (1 + 25/100) = 420 × 1.25 = ₹525

Let M.P. = 420 × (1 + m/100)

After 10% discount, S.P. = M.P. × 0.90 → 0.9 × 420 × (1 + m/100) = 525

Divide both sides by 0.9 × 420:
1 + m/100 = 525 / (0.9 × 420) = 525 / 378 = 1.388888...

m/100 = 0.388888... → m = 38.8888...% ≈ 38.89%

So mark about 38.89% above cost.

 

Question 15:

A shopkeeper bought an article at 20% discount on the printed price (marked price). He sells it at the marked price. Find his profit percentage.

Solution:

Let M.P. = ₹100

He bought at 20% discount on M.P. → C.P. = 100 × (1 – 20/100) = 100 × 0.8 = ₹80

He sells at M.P. = ₹100

Profit = 100 – 80 = ₹20

Profit% = (20 / 80) × 100 = 25% → 25% Profit

 

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.

 

Frequently Asked Questions On Profit and Loss Questions

1. What is a profit and a loss?

Ans:

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

 

2. What is the formula for profit and loss?

 Ans:

• Profit = Selling Price - Cost Price

• Loss = Cost Price - Selling Price

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

• Loss % = (Loss / Cost Price) × 100

 

3. What does P&L mean?

Ans:

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?

Ans:

• 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

 

5. How to calculate losses?

Ans:

Use the formula:

Loss = Cost Price - Selling Price

To find the percentage loss:

Loss% % = (Loss / Cost Price) × 100

 

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