Profit, Loss and Discount Formulas: Complete Formula Sheet for SSC, RRB, Banking & Defence Exams

We have already covered the basic concepts, solved examples and practice questions in our Profit, Loss and Discount chapter. 

This page is dedicated to Profit, Loss and Discount formulas so that you can quickly revise the important formulas and solve questions faster in examinations.

Profit, Loss and Discount formulas are frequently used in SSC CGL, SSC CHSL, SSC MTS, RRB NTPC, RRB Group D, Banking, Defence and other competitive examinations. 

This page provides a quick revision sheet of all important formulas related to Profit Percentage, Loss Percentage, Discount, Marked Price, Successive Discount, False Weight and GST. For complete concept explanations, chapter-wise study material, and additional learning resources, you can also explore our Quantitative Aptitude Notes, Quantitative Aptitude Formula Section, Math Calculators, and Quantitative Aptitude Syllabus sections.

Most Important Profit, Loss and Discount Formulas for SSC & RRB

Quick revision for all formulas.

*Remember this rule for competitive exams: if two articles are sold at the same selling price, one at x% profit and the other at x% loss, the final outcome is always an overall loss.

Profit when SP is more than CP i.e SP>CP

Loss when SP is less than CP i.e CP>SP

How did we get Selling price (profit)=

Profit % = ((SP − CP)/CP) × 100

Profit %/100 = (SP − CP)/CP

Profit %/100

= SP/CP − 1

SP/CP = 1 + Profit %/100

SP = CP × (1 + Profit %/100)

And similarly

Selling Price (loss)

Loss %= ((CP-SP)/CP)x100

Loss %=(1-SP/CP)x100

Loss %/100= 1-SP/CP

SP/CP= (1- Loss %/100)

SP= CPx(1-Loss %/100)

And similarly cost price (profit) and  cost price (loss) formulas are derived.

Example 1: Understanding Profit, Loss, Profit % and Loss %

An RRB NTPC PYQ book is purchased for ₹80.

Case 1: Book Sold at ₹95

Here,

Cost Price (CP) = ₹80

Selling Price (SP) = ₹95

Since the selling price is greater than the cost price, there is a profit.

Profit

= SP − CP

= 95 − 80

= ₹15

Profit Percentage:

Profit %

= (Profit ÷ CP) × 100

= (15 ÷ 80) × 100

= 18.75%

Therefore,

Profit = ₹15

Profit % = 18.75%

Case 2: Book Sold at ₹75

Here,

Cost Price (CP) = ₹80

Selling Price (SP) = ₹75

Since the selling price is less than the cost price, there is a loss.

Loss

= CP − SP

= 80 − 75

= ₹5

Loss Percentage:

Loss %

= (Loss ÷ CP) × 100

= (5 ÷ 80) × 100

= 6.25%

Therefore,

Loss = ₹5

Loss % = 6.25%

Example 2: Finding Selling Price When Profit Percentage is Given

A shopkeeper near an SSC CGL coaching centre is selling a MathsByNITian Maths Series book at a 10% profit. The cost price of the book is ₹100.

Find the selling price.

Solution

Given:

CP = ₹100

Profit % = 10%

Using the formula:

Selling Price

= CP × (1 + Profit %/100)

Substituting the values:

= 100 × (1 + 10/100)

= 100 × 11/10

= ₹110

Answer:

Selling Price = ₹110

Example 3: Finding Selling Price When Loss Percentage is Given

The same shopkeeper sells a MathsByNITian Maths Series book at a 10% loss. The cost price remains ₹100.

Find the selling price.

Solution

Given:

CP = ₹100

Loss % = 10%

Using the formula:

Selling Price

= CP × (1 − Loss %/100)

Substituting the values:

= 100 × (1 − 10/100)

= 100 × 9/10

= ₹90

Answer:

Selling Price = ₹90

Example 4: Finding Cost Price When Profit Percentage and Selling Price are Given

A Banking aspirant purchased a quantitative aptitude book from a bookstore near a banking coaching institute. The shopkeeper sold the book for ₹1,200 at a 20% profit.

Find the cost price of the book.

Solution

Given:

Selling Price (SP) = ₹1,200

Profit % = 20%

Using the formula:

Cost Price (Profit)

= SP ÷ (1 + Profit %/100)

Substituting the values:

= 1200 ÷ (1 + 20/100)

= 1200 ÷ 1.2

= ₹1,000

Answer:

Cost Price = ₹1,000

Example 5: Finding Cost Price When Loss Percentage and Selling Price are Given

A candidate preparing for IBPS PO sold a banking guide book for ₹900. The sale resulted in a 10% loss.

Find the cost price of the book.

Solution

Given:

Selling Price (SP) = ₹900

Loss % = 10%

Using the formula:

Cost Price (Loss)

= SP ÷ (1 − Loss %/100)

Substituting the values:

= 900 ÷ (1 − 10/100)

= 900 ÷ 0.9

= ₹1,000

Answer:

Cost Price = ₹1,000

Discount Formulas And Application

Example 6: Discount, Discount Percentage and Selling Price

A bookshop near Kashmiri Gate Metro Station, Delhi, is selling an SSC CGL practice book.

The Marked Price (MP) of the book is ₹500 and it is sold for ₹450.

Find:

1. The discount offered.
2. The discount percentage.

Solution

Given:

Marked Price (MP) = ₹500

Selling Price (SP) = ₹450

Step 1: Find Discount

Using the formula:

Discount

= MP − SP

= 500 − 450

= ₹50

Step 2: Find Discount Percentage

Using the formula:

Discount %

= (Discount ÷ MP) × 100

= (50 ÷ 500) × 100

= 10%

Answer

Discount = ₹50

Discount % = 10%

Selling Price = ₹450

Successive Discount Formulas

Example 7: Equivalent Discount for Two Successive Discounts

After the declaration of the IBPS Clerk results, a bookstore offers two successive discounts of 20% and 10% on a banking preparation book.

Find the equivalent discount.

Solution

Here,

a = 20%

b = 10%

Using the formula:

Equivalent Discount

= a + b − ab/100

Substituting the values:

= 20 + 10 − (20 × 10)/100

= 20 + 10 − 2

= 28%

Why do we subtract?

If we simply add the discounts,

20% + 10% = 30%

This is incorrect because the second discount of 10% is applied on the reduced price, not on the original marked price.

The term:

ab/100

represents the overlapping discount counted twice when we directly add the two discounts.

Therefore, we subtract it once.

Answer

Equivalent Discount = 28%

SSC/RRB/Defence/Banking/NDA/CDS/Agniveer Shortcut

Let the marked price of the book be ₹100.

First discount = 20%

Book Price

= 100 − 20

= ₹80

Second discount = 10%

Book Price

= 80 − 10% of 80

= 80 − 8

= ₹72

Therefore,

Equivalent Discount

= 100 − 72

= ₹28

Hence,

Equivalent Discount = 28%

Example 8: Equivalent Discount for Three Successive Discounts

After the declaration of the IBPS PO results, a bookstore offers three successive discounts of 20%, 10%, and 5% on banking examination books.

Find the equivalent discount.

Solution

Here,

a = 20%

b = 10%

c = 5%

Using the formula:

Equivalent Discount

= a + b + c

− ab/100

− bc/100

− ac/100

+ abc/10000

Substituting the values:

= 20 + 10 + 5

− (20 × 10)/100

− (10 × 5)/100

− (20 × 5)/100

+ (20 × 10 × 5)/10000

= 35

− 2

− 0.5

− 1

+ 0.1

= 31.6%

Why are some terms subtracted and one added?

When we directly add:

a + b + c

the common portions are counted more than once.

Therefore,

ab/100

bc/100

ac/100

are subtracted.

However, after subtracting these three terms, the common portion represented by

abc/10000

gets removed one extra time.

Hence it is added back.

Answer

Equivalent Discount = 31.6%

SSC/RRB/Defence/Banking/NDA/CDS/Agniveer Shortcut

Let the marked price of the book be ₹100.

First Discount = 20%

Book Price

= 100 − 20

= ₹80

Second Discount = 10%

Book Price

= 80 − 10% of 80

= 80 − 8

= ₹72

Third Discount = 5%

Book Price

= 72 − 5% of 72

= 72 − 3.6

= ₹68.4

Therefore,

Book Price reduced from ₹100 to ₹68.4

Hence,

Equivalent Discount

= 100 − 68.4

= 31.6%

False Weight (Dishonest Shopkeeper) Formulas and Applications

In some competitive examination questions, a shopkeeper claims to sell a certain quantity of goods but actually gives a lower quantity. Such questions are commonly known as False Weight or Dishonest Shopkeeper questions.

For example: 1 kg claimed but only 900 g actually given or 1 kg claimed 950 g given or like that.

So, the customer actually pays for 1 kg weight of the item, but he/she gets only 900 or 950 grams of the item, making the shopkeeper earning more.

Example 9: False Weight (Dishonest Shopkeeper)

A shopkeeper in Mukherjee Nagar, Delhi, sells sugar at ₹72 per kg. However, instead of giving 1 kg, he gives only 800 g of sugar while charging the customer for 1 kg.

Find the profit percentage earned by the shopkeeper due to false weight.

Solution

Here,

True Weight = 1000 g

False Weight = 800 g

Cost Price of 1000 g sugar = ₹72

Cost Price of 800 g sugar

= 72 × 800/1000

= ₹57.6

SP = ₹72

Profit =SP-CP= 72-57.6= ₹14.4

Profit %

= (14.4/57.6) ×100

= 25%

Answer

Profit Percentage = 25%

GST Formulas with Application

Example 10: GST Amount, Price Including GST and Original Price

A student preparing for SSC CGL purchases a MathsByNITian Arithmetic Book from a bookstore in Mukherjee Nagar, Delhi. The original price of the book is ₹2,500 and GST is charged at 18%.

Find:

1. GST Amount
2. Price Including GST
3. Verify the Original Price using the GST-inclusive price

Solution

Given:

Original Price = ₹2,500

GST = 18%

Step 1: Find GST Amount

Using the formula:

GST Amount

= GST% × Original Price / 100

= (18 × 2500)/100

= ₹450

Step 2: Find Price Including GST

Using the formula:

Price Including GST

= Original Price × (1 + GST%/100)

= 2500 × (1 + 18/100)

= 2500 × 1.18

= ₹2,950

Step 3: Verify the Original Price

Using the formula:

Original Price

= Inclusive Price × 100/(100 + GST%)

= 2950 × 100/(100 + 18)

= 2950 × 100/118

= ₹2,500

Practice more GST questions at GST Questions with Answers and Solutions section.

Equal Profit & Equal Loss Application

This shortcut applies when two items are sold at the same selling price, with one sold at a profit of x% and the other at a loss of x%. In this condition, the seller always incurs an overall loss.

Example 11:

A railway contractor at Cuttack Railway Station supplied two consignments of steel rails to the Indian Railways. Both consignments were sold at the same selling price of ₹12,000 each. On the first consignment, the contractor earned a 20% profit, while on the second consignment, he incurred a 20% loss.

Find the contractor’s overall profit or loss percentage.

Solution

First Consignment

Given:

Selling Price (SP) = ₹12,000

Profit = 20%

Using the formula:

SP = CP × (1 + Profit%/100)

Substitute the values:

12000 = CP × (1 + 20/100)

12000 = CP × 1.20

CP = 12000 ÷ 1.20

CP = 10000

Therefore, the Cost Price (CP) = ₹10,000.

Second Consignment

Given:

Selling Price (SP) = ₹12,000

Loss = 20%

Using the formula:

SP = CP × (1 − Loss%/100)

Substitute the values:

12000 = CP × (1 − 20/100)

12000 = CP × 0.80

CP = 12000 ÷ 0.80

CP = 15000

Therefore, the Cost Price (CP) = ₹15,000.

Overall Profit or Loss

Total Cost Price

= 10000 + 15000

= 25000

Total Selling Price

= 12000 + 12000

= 24000

Overall Loss

= 25000 − 24000

= 1000

Using the Loss Percentage formula:

Loss % = (Loss ÷ Total Cost Price) × 100

Substitute the values:

= (1000 ÷ 25000) × 100

= 4%

Answer: The railway contractor incurred an overall loss of 4%.

Shortcut for SSC/RRB/Defence/Banking

Overall Loss % = x² ÷ 100

Here,

= 20² ÷ 100

= 400 ÷ 100

= 4%

Answer: Overall Loss = 4%.

FAQs

1. What is the formula of profit percentage?

The profit percentage is calculated by formula: Profit %= (Profit ÷ CP) × 100

2. What is the formula of discount percentage?

The discount percentage can be calculated with the formula: Discount % =(Discount ÷ MP) × 100

3. What is the successive discount formula?

Successive discount formula= a+b-ab/100

4. What is the GST formula?

Formula to calculate GST is;

GST Amount =(GST% × Original Price)/100

Important Resources Related to Profit, Loss & Discount

1. Profit, Loss and Discount: Formula, Questions, Tricks & Examples for SSC, RRB
2. Percentage: Meaning, Formula, Examples & Questions for Exams
3. Ratio and Proportion
4. Profit & Loss Questions with Answers and Solutions
5. Discount Questions with Answers and Solutions
6. Dishonest Shopkeeper Questions with Answers and Solutions
7. Successive Discount Questions with Answers and Solutions
8. Profit, Loss & Discount Practice Questions
9. Profit, Loss & Discount PYQs SSC, RRB, Banking & Defence Exams (Solved)
10. Simple Interest & Compound Interest Formula with Examples and Explanations