Profit, Loss and Discount is one of the most important chapters of Arithmetic for SSC, RRB, Banking, Defence and other competitive examinations. Questions from this topic are regularly asked in exams such as SSC CGL, SSC CHSL, SSC MTS, RRB NTPC, RRB Group D, Banking and Defence recruitment exams.
The concepts of Profit, Loss and Discount are closely related to Percentage and Ratio & Proportion, making this chapter essential for solving a wide range of arithmetic questions quickly and accurately.
In this chapter, you will learn all the important concepts, formulas and shortcuts related to:
- Cost Price (CP)
- Selling Price (SP)
- Profit
- Loss
- Profit Percentage
- Loss Percentage
- Discount
- Marked Price
- Successive Discount
- False Weight
We have also included solved examples, practice questions, MCQs and previous year questions (PYQs) to help you strengthen your concepts and improve your exam performance.
Whether you are preparing for SSC, RRB, Banking or Defence exams, mastering Profit, Loss and Discount can significantly improve your arithmetic score and overall accuracy.
Let us begin by understanding the basic concepts and formulas of Profit, Loss and Discount.
What is the Cost Price?
The price at which we buy a product or item is called the Cost Price. It is represented by CP.
For example, if a shopkeeper buys a pen for ₹10, then:
CP = ₹10
What is the Selling Price?
The price at which a product or item is sold is called the Selling Price. It is represented by SP.
For example, if the pen is sold for ₹12, then:
SP = ₹12
What is the Marked Price?
The price printed on a product by the shopkeeper or manufacturer is called the Marked Price (MP).
The marked price is usually higher than the selling price because discounts may be offered to customers.
For example:
Marked Price = ₹500
Solve marked price questions at our Marked Price Questions with Answers and Solutions section.
What is Profit?
Suppose you bought a pen for ₹10 and sold it to your friend for ₹12. Since the selling price is greater than the cost price, you have earned a profit of ₹2.
Cost Price (CP) = ₹10
Selling Price (SP) = ₹12
Therefore,
Profit = SP − CP
= 12 − 10
= ₹2
Whenever the selling price is more than the cost price, there is a profit.
Example 1:
Ravi purchased 20 SSC preparation books for ₹250 each from a wholesale market. He sold each book for ₹300.
Find:
- The total Cost Price (CP)
- The total Selling Price (SP)
- The Profit earned
- The Profit Percentage
Solution:
Step 1: Find the Total Cost Price
Cost Price of 1 book = ₹250
Number of books = 20
Total CP = 250 × 20 = ₹5,000
Step 2: Find the Total Selling Price
Selling Price of 1 book = ₹300
Total SP = 300 × 20 = ₹6,000
Step 3: Find the Profit
Profit = SP − CP
= 6,000 − 5,000
= ₹1,000
Step 4: Find the Profit Percentage
Profit % = (Profit ÷ CP) × 100
= (1,000 ÷ 5,000) × 100
= 20%
Answer:
- Total Cost Price = ₹5,000
- Total Selling Price = ₹6,000
- Profit = ₹1,000
- Profit Percentage = 20%
What is Loss?
Suppose you bought a pen for ₹10 but could only sell it for ₹8. Since the selling price is less than the cost price, you incur a loss of ₹2.
Cost Price (CP) = ₹10
Selling Price (SP) = ₹8
Therefore,
Loss = CP − SP
= 10 − 8
= ₹2
Whenever the selling price is less than the cost price, there is a loss.
Example 2:
Neha booked 10 railway tickets for SSC aspirants to travel to an examination center. The total cost of the tickets was ₹8,000. Due to cancellation, she could recover only ₹7,200 by selling the tickets.
Find:
- The Cost Price (CP)
- The Selling Price (SP)
- The Loss incurred
- The Loss Percentage
Solution:
Given:
Cost Price (CP) = ₹8,000
Selling Price (SP) = ₹7,200
Step 1: Find the Loss
Loss = CP − SP
= ₹8,000 − ₹7,200
= ₹800
Step 2: Find the Loss Percentage
Loss % = (Loss ÷ CP) × 100
= (800 ÷ 8,000) × 100
= 10%
Answer:
- Cost Price (CP) = ₹8,000
- Selling Price (SP) = ₹7,200
- Loss = ₹800
- Loss Percentage = 10%
What is a Discount?
When a seller reduces the marked price of an item, the reduction is called a discount.
The formula for discount is:
Discount = Marked Price − Selling Price
Discount = MP − SP
Example 3:
The marked price of an item is ₹600, and it is sold for ₹540.
Discount = MP − SP
= 600 − 540
= ₹60
Discount Percentage Formula
Discount Percentage= (Discount/Marked Price)x100
=(60/600)x100
Therefore, the discount offered is ₹60 or 10%.
Example 4:
A shopkeeper marked a packet of 10 pens at ₹500. During a back-to-school sale, he offered a 20% discount on the Marked Price.
Find:
- The Marked Price (MP)
- The Discount Amount
- The Selling Price after discount
- If the Cost Price of the packet is ₹350, calculate the Profit earned.
Solution:
Given:
Marked Price (MP) = ₹500
Discount = 20%
Cost Price (CP) = ₹350
Step 1: Find the Discount Amount
Discount Amount = 20% of ₹500
= (20/100) × 500
= ₹100
Step 2: Find the Selling Price
Selling Price = Marked Price − Discount
= ₹500 − ₹100
= ₹400
Step 3: Find the Profit
Profit = Selling Price − Cost Price
= ₹400 − ₹350
= ₹50
Answer:
- Marked Price (MP) = ₹500
- Discount Amount = ₹100
- Selling Price = ₹400
- Profit = ₹50
Profit & Loss Formula Table
| Concept | Formula |
| Profit | SP − CP |
| Loss | CP − SP |
| Profit % | (Profit/CP) × 100 |
| Loss % | (Loss/CP) × 100 |
| Discount | MP − SP |
| Discount % | (Discount/MP) × 100 |
| SP (Profit) | CP × (100 + Profit%)/100 |
| SP (Loss) | CP × (100 − Loss%)/100 |
Successive Discount Questions:
A bookstore offering RRB NTPC preparation books announces two successive discounts of 20% and 10% on a book whose marked price is ₹1,500.
Find:
- The selling price after the first discount
- The final selling price after both discounts
- The total discount amount
- The equivalent single discount percentage
Solution:
Given:
Marked Price (MP) = ₹1,500
First Discount = 20%
Second Discount = 10%
Step 1: Find the Selling Price after the First Discount
First Discount Amount
= 20% of ₹1,500
= (20/100) × 1,500
= ₹300
Selling Price after First Discount
= ₹1,500 − ₹300
= ₹1,200
Step 2: Find the Final Selling Price after the Second Discount
Second Discount Amount
= 10% of ₹1,200
= (10/100) × 1,200
= ₹120
Final Selling Price
= ₹1,200 − ₹120
= ₹1,080
Step 3: Find the Total Discount Amount
Total Discount
= Marked Price − Final Selling Price
= ₹1,500 − ₹1,080
= ₹420
Step 4: Find the Equivalent Single Discount Percentage
Equivalent Discount %
= (Total Discount ÷ Marked Price) × 100
= (420 ÷ 1,500) × 100
= 28%
SSC/RRB/Defence/Banking Short cut
For two successive discounts of 20% and 10%:
Equivalent Discount
= 20 + 10 − (20 × 10)/100
= 30 − 2
= 28%
Thus, the equivalent single discount is 28%.
Equivalent Discount %= a+b-(ab/100)
where:
- a = First discount %
- b = Second discount %
For more questions on successive discounts check our successive discounts questions and answers section.
False Weight Question
A shopkeeper claims to sell 1 kg of groundnuts for ₹180, but he uses a false weight of 900 grams instead of 1 kg.
Find:
- The Cost Price of 900 grams if the actual Cost Price of groundnuts is ₹150 per kg
- The Selling Price of 900 grams
- The Profit earned on each sale
- The Profit Percentage
Solution:
Given:
Actual Cost Price of 1 kg groundnuts = ₹150
False Weight Used = 900 grams
Selling Price charged for “1 kg” = ₹180
Step 1: Find the Cost Price of 900 grams
Since 1 kg = 1000 grams,
Cost Price of 900 grams
= ₹150 × (900/1000)
= ₹135
Step 2: Find the Selling Price of 900 grams
The shopkeeper charges ₹180 while giving only 900 grams.
Therefore,
Selling Price of 900 grams = ₹180
Step 3: Find the Profit Earned
Profit = Selling Price − Cost Price
= ₹180 − ₹135
= ₹45
Step 4: Find the Profit Percentage
Profit %
= (Profit ÷ Cost Price) × 100
= (45 ÷ 135) × 100
= 33.33%
Find more question on false weight/dishonest shopkeeper; Dishonest Shopkeeper Questions with Answers and Solutions
Shortcut Method
When a shopkeeper gives only 900 grams instead of 1000 grams and sells it at the cost of 1 kg:
Cost Price of goods sold
= ₹150 × (900/1000)
= ₹135
Profit
= ₹180 − ₹135
= ₹45
Profit %
= (45 ÷ 135) × 100
= 33.33%
Practice Question on Profit, Loss and Discount
- A competitive exam book marked 800 Rs is sold at 760 Rs. What is the discount and discount %?
- A bookstore purchased a set of RRB ALP preparation books for ₹1,200 and sold it for ₹1,500.
Find:
- The Cost Price (CP)
- The Selling Price (SP)
- The Profit earned
- The Profit Percentage
3. A candidate appearing for the SSC Stenographer Exam booked railway tickets and accommodation for ₹4,500. Due to the exam being postponed, he could recover only ₹3,825 through cancellations and refunds.
Find:
- The Cost Price (CP)
- The Selling Price (SP)
- The Loss incurred
- The Loss Percentage
Check our detailed Profit, Loss and Discount Practice Questions section and SSC, RRB, Defence, Banking PYQ section to do more practice and strengthen the concept.
FYQ on Profit, Loss and Discount
1. What is profit, loss and discount?
Profit, when selling price is more than buying price or cost price: SP>CP
Loss: when selling price is less than buying price or cost price: SP<CP
Discount: Price reduction offered on marked price= MP-SP
2. Is there a profit, loss and discount section in SSC, RRB, defence, banking, NDA, CDS exams?
Yes, they are asked every year in these exams.
3. How much time do we need to complete the profit, loss and discount chapter?
If you practice daily then within a week or in 10 days you can improve your learning of profit, loss and discount sections.
Related Resources to Profit, Loss & Discount
- Percentage: Meaning, Formula, Examples & Questions for Exams
- Ratio and Proportion
- Profit, Loss and Discount Formulas: Complete Formula Sheet for SSC, RRB, Banking & Defence Exams
- Profit & Loss Questions with Answers and Solutions
- Discount Questions with Answers and Solutions
- Dishonest Shopkeeper Questions with Answers and Solutions
- GST Questions with Answers and Solutions