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Profit & Loss in CAT 2025: Only 3 Formulas Needed for All Variations
Ongoing Event
CAT Admit Card Date:12 Nov' 25 - 30 Nov' 25
Do you ever think the secondary school level topics like Profit and Loss can be so important for you, while you are going to take the CAT exam? In the quantitative aptitude section of the CAT exam, the arithmetic section is very important, and the subtopic profit and loss is a key topic. In this topic, you may find around 15+ formulas to solve the questions based on successive discounts, marked price tricks, or faulty weight problems. In this article, you will find
This Story also Contains
- Introduction to Profit and Loss for CAT
- How to Solve Profit and Loss in CAT Using These Formulas
- Solved Past 5 Years’ Questions with Solutions of Profit and Loss for CAT
- How to Prepare for Profit and Loss in the CAT Exam
- CAT 2025 Preparation Resources by Careers360
- 3 formula strategies to solve the problems in each variation
- How to apply these formulas in different scenarios?
- How to improve accuracy?
- Memory-based approaches to solving the CAT questions
Introduction to Profit and Loss for CAT
To understand the topic, you must understand the basic definitions first, like
CP (Cost Price): It is the price at which an article is purchased.
SP (Selling Price): It is the price at which an article is sold.
MP (Marked Price or List Price): It is the price marked on the article. Discounts are generally calculated on this price.
Profit or Gain: When SP > CP, the seller makes a profit.
Profit = SP - CP
Loss: When CP > SP, the seller incurs a loss.
Loss = CP - SP
Discount: It's a reduction given on the marked price (MP).
Discount = MP – SP
Also, you should understand the question types that are being asked in the CAT
-
Questions based on CP, SP, and MP
When CP, discount%, Profit% are given, and other variables like SP, MP, etc need to be calculated.
-
Questions based on successive discounts
When two or more discounts are given successively, and you have been asked to calculate the SP, MP, or net discount percent.
-
Questions based on Faulty weight and Adulteration
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowIn these types of questions, the final profit% is asked after adulteration, or sometimes the adulteration percent is asked when the final profit percent is given.
Why Profit and Loss is important in CAT Quant
-
The CAT quant section has one or two questions from this topic every year, ranging in difficulty from medium to high level. So, this topic should be practised more.
-
From the analysis of CAT previous years' question papers, we noticed that, along with direct questions from Profit and Loss, Caselet Data Interpretation based on this is also asked.
Weightage of Profit & Loss in CAT over the years
We have analysed the previous 5 years' papers of CAT to find out the weightage and CAT exam pattern of the questions form profit and loss that are asked in the exam. Here is a summary of the weightage of questions of profit and loss year-wise and slot-wise.
|
S. No. |
Year |
Slot |
Number of questions |
|
1 |
2020 |
1 |
1 |
|
2 |
2020 |
2 |
1 |
|
3 |
2020 |
3 |
1 |
|
4 |
2021 |
1 |
1 |
|
5 |
2021 |
2 |
2 |
|
6 |
2021 |
3 |
1 |
|
7 |
2022 |
1 |
2 |
|
8 |
2022 |
2 |
0 |
|
9 |
2022 |
3 |
0 |
|
10 |
2023 |
1 |
1 |
|
11 |
2023 |
2 |
2 |
|
12 |
2023 |
3 |
1 |
|
13 |
2024 |
1 |
1 |
|
14 |
2024 |
2 |
1 |
|
15 |
2024 |
3 |
1 |
Common mistakes students make in Profit & Loss CAT questions
It is important to understand the common mistakes in the CAT exam that a student makes while solving the Profit and Loss questions.
|
Common Mistakes |
How to Rectify |
|
Ignoring basic concepts |
Understand all the basic definitions and formulas, and practice questions based on them |
|
Misinterpreting the base |
Usually, students calculate the profit percent on the selling price instead of the cost price. So, it is very important to understand that the profit is always calculated on CP, discount is always calculated on MP. |
|
Mistakes in converting percentages into fractions |
Practice the percentage to fraction conversion and vice versa. |
|
Errors in finding successive discounts |
It is important to understand whether the successive discounts are needed or not. You should focus more and practice more |
|
When questions involve two or more concepts, students often make mistakes |
Practice questions based on the concept amalgam. |
The Only 3 Profit and Loss Formulas You Need for CAT
There are 3 basic formulas in profit and loss that need to be understood to solve any question in Profit and loss. The rest are the variations of the questions.
Formula 1 (Relating SP, CP, and Profit/Loss)
Profit $\% = \frac{\text{Profit}}{\text{CP}} \times 100$, where CP is the cost price.
Loss $\% = \frac{\text{Loss}}{\text{CP}} \times 100$, where CP is the cost price.
Profit $= \text{SP} - \text{CP}$, Loss $= \text{CP} - \text{SP}$
Other Variations of this formula:
$\text{SP} = \text{CP} \times \frac{100 + \text{Profit}\%}{100}$
Key Usage: Basic P&L questions, cost-price/selling-price direct problems.
Example: A shopkeeper buys a book for ₹400 and sells it at ₹460. Find profit %.
Profit = $60$, $CP = 400 \Rightarrow$ Profit $\% = \dfrac{60}{400} \times 100 = 15\%$.
Formula 2 (Relating SP, MP, and Discount)
Discount % = $\dfrac{Discount}{MP} \times 100$, where $MP$ is the marked price.
Discount = $MP - SP$
Other Variation:
$SP = MP \times \dfrac{100 - Discount\%}{100}$
Key Usage: Marked price, successive discounts, successive profit/loss.
Example: A shopkeeper gives two successive discounts of $40\%$ and $30\%$ respectively. Find the effective discount %.
Let $MP = 100$. After 1st discount, price $= 60$. After second discount of $30\%$, final $SP = 60 \times 0.7 = 42$.
Net Discount% $= \dfrac{100 - 42}{100} \times 100 = 58\%$.
Alternate solution (Trick):
Net discount% $= 40 + 30 - \dfrac{40 \times 30}{100} = 70 - 12 = 58\%$
Formula 3 (Relating MP, CP, and markup value)
Markup% = $\dfrac{Markup\ value}{CP} \times 100$
Other Variation:
$SP = MP \times \dfrac{100 - Discount\%}{100}$
Key Usage: Marked price, hike in the price of value, successive increase in the price.
Example: A man marked up the price on one article by $20\%$ and lost $10\%$ on the marked price while selling. Find net % gain/loss.
Let $CP = 100$. After increase of $20\%$, price $= 120$. After second transaction, final $SP = 120 \times 0.9 = 108$.
Net gain% $= \dfrac{108 - 100}{100} \times 100 = 8\%$.
How to Solve Profit and Loss in CAT Using These Formulas
A few points must be remembered before solving questions using these 3 formulas
1. Profit or loss percent is always calculated on the cost price.
2. Discount percent is always calculated on the marked price.
3. The markup percent is always calculated on the cost price.
Also, there are some prerequisite conditions:
Hands-on percentage to fraction conversion and vice versa.
Step-by-step approach to Profit & Loss CAT questions
Consider the following example:
Question: A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to: [CAT 2024]
Solution:
Step 1: First, understand the problem statement and the information given in the question.
In this question, the markup percent is to be calculated.
Given:
Targeted Profit % = 20%
Sold 5 kg at the targeted price.
Sold 15 Kg at a discount of 10%.
3 kg of sugar is wasted.
Now, we need to find the percentage increase in the price of the remaining sugar so that the total profit is 15%.
Step 2: Identify the concept required to solve the question.
Formula 1 should be used in between
Profit/Loss % = $\dfrac{Profit\ or\ Loss}{CP} \times 100\%$, where $CP$ is the cost price.
Formula 2 (used in between):
Discount % = $\dfrac{Discount}{MP} \times 100\%$, where $MP$ is the marked price.
Formula 3 (used in the end):
Markup % = $\dfrac{Markup\ Value}{CP} \times 100\%$, where $CP$ is the cost price.
Step 3: Apply the concept/formula to find the unknown.
Final Solution:
Let the cost price of 1kg of sugar = Rs 100
The total cost price of 35 kg = Rs 3500
Marked price per kg = Rs 120
Given, the final profit is 15%. So, Final SP of 35 kg = 3500 × 1.15 = Rs 4025
First 5 kg's are sold at 20% marked-up price, SP1 = 5 × 100 × 1.2 = Rs 600
Next 15 kg are sold after giving 10% discount, SP2 = 15 × 100 × 1.2 × 0.9 = Rs. 1620
3 kg of sugar got wasted
$\Rightarrow 23 \text{ kg of sugar was sold at } Rs.\ (600 + 1620) = Rs.\ 2220$
The remaining $12 \text{ kg}$ should be sold at $Rs.\ (4025 - 2220) = Rs.\ 1805$
$\Rightarrow SP \text{ of 1 kg } = \dfrac{1805}{12} \approx Rs.\ 150$
Hence, the seller should further mark up by
$\dfrac{150 - 120}{120} \times 100 = 25\%$
Identifying shortcut opportunities in CAT Quant
Here are a few shortcuts that can be helpful to solve the questions effectively and save time during the exam.
|
Concept |
Shortcut |
|
To find the net profit or loss percent if the cost price of n articles is the same. |
Average of all profit and loss percentages. Profit percentages are taken as positive, while loss percentage is taken as negative. |
|
To find the net profit or loss percent if the selling price of 2 articles is the same and the profit % (x%) and loss % (x%) are the same. |
$\text{Net Loss %} = \dfrac{x^2}{100}$ |
|
Net discount if there are two successive discounts of $R_1\%$ and $R_2\%$. |
$\text{Net } \% = R_1 + R_2 - \dfrac{R_1 R_2}{100}$ |
Solved Past 5 Years’ Questions with Solutions of Profit and Loss for CAT
Q.1) Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is
Solution:- [Expected time to be taken: 45 to 60 seconds, Level of Difficulty: Moderate]
Let the cost price for Bina be $x$.
Bina sells to Shyam at a 19% loss:
$4860 = x - \frac{19}{100}x = \frac{81}{100}x$
So, $x = \frac{4860 \times 100}{81} = 6000$
Now, let the selling price to Hari be $y$.
If Bina had sold to Shyam at Hari's price and made 17% profit:
$y = x + \frac{17}{100}x = \frac{117}{100} \times 6000 = 7020$
So, Shyam bought at Rs. 4860 and sold at Rs. 7020
Therefore, his profit is: $7020 - 4860 = 2160$
Hence, the correct answer is $2160$.
Q.2) Gopi marks a price on a product in order to make $20 %$ profit. Ravi gets $10 %$ discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
A) 15
B) 25
C) 10
D) 10
Solution:- [Expected time to be taken: 45 seconds, Level of Difficulty: Easy]
Let the cost price of the product be $100x$.
Gopi wants to make a $20\%$ profit,
so the marked price (MP) is:
$
\text{MP} = 100x \times \left(1 + \frac{20}{100}\right) = 120x
$
Ravi gets $10$ % discount on the marked price, so the selling price (SP) is:
$
\text{SP} = 120x \times \left(1 - \frac{10}{100}\right) = 120 \times \frac{90}{100} = 108x
$
Now, the discount Ravi gets = $120x - 108x = 12x$
But the question says Ravi saves Rs 15,
So, $12x=15$
$⇒x=\frac{15}{12}=\frac54$
The profit made by Gopi = $108x - 100x = 8x= 10$ rupees.
Hence, the correct answer is option 3.
Q.3) Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to:
A) 42%
B) 47%
C) 45%
D) 45%
Solution:- [Expected time to be taken: 75 to 90 seconds, Level of Difficulty: Moderate to Hard]
Let the original selling price of both A and B be Rs 100.
So, the cost price of A (Profit of 20%) = $\frac{5}{6} \times 100 = \frac{250}{3}$
And, Cost price of B (Loss of 10%) = $\frac{10}{9} \times 100 = \frac{1000}{9}$
After an increase in the selling price by some value, the profit on object B is 10%.
So, the new selling price = 110% of the cost price of B
= $\frac{1000}{9} \times \frac{110}{100} = \frac{1100}{9}$
Profit of A = $\frac{1100}{9} - \frac{250}{3} = \frac{350}{9}$
Profit percentage of A = $\frac{\frac{350}{9}}{\frac{250}{3}} \times 100 = 46.67$% (Nearest to 47%)
Hence, the correct answer is option (2).
Q.4) Minu purchased a pair of sunglasses for Rs. 1000 and sold them to Kanu for 20% profit. Then, Kanu sells it back to Minu at a 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs. 500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
A) 35.42%
B) 31.25%
C) 52%
D) 52%
Solution:- [Expected time to be taken: 60 to 75 seconds, Level of Difficulty: Moderate]
Initial Cost Price for Minu = 1000
Cost Price to Kanu = 120% of 1000 = 1200
Profit made by Minu = 1200 – 1000 = 200
Again Minu purchased at 80% of 1200 = 960
The total profit made by Manu is 500. So, profit made when she sold it to Tanu = 500 – 200 = 300
Final Selling Price for Minu when sold to Tanu = 960 + 300 = 1260
Profit percent = $\frac{300}{960}$ $\times$ 100 = 31.25%
Hence, the correct answer is option (2).
Q.5) Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of Rs. 1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of Rs. 744. Then the amount, in rupees, that she had spent in buying almonds is:
A) 1680
B) 1176
C) 2520
D) 2520
Solution:- [Expected time to be taken: 90 to 120 seconds, Level of Difficulty: Hard]
It is given, $7C = 30P = 9A$ and Ankita bought 4C, 14P and 6A.
Let $7C = 30P = 9A = 630k$
$⇒C = 90k, P = 21k$, and $A = 70k$
Cost price of 4C, 14P and 6A $= 4(90k)+14(21k)+6(70k) = 1074k$
Marked up price $= 1074k + 1752$
So,
$\begin{aligned} & \text { S.P }=\frac{1}{6}(1074 k+1752)+\left(\frac{4}{5}\right)\left(\frac{5}{6}\right)(1074 k+1752)=\frac{5}{6}(1074 k+1752) \\ & ⇒\text { S.P-C.P }=\text { profit } \\ & ⇒1460-\frac{1074 k}{6}=744 \\ & ⇒\frac{1074 k}{6}=716\end{aligned}$
$⇒k = 4$
Money spent on buying almonds = 420k = 420 × 4 = Rs 1680
The correct answer is Rs. 1680.
Q.6) Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at Rs 308.32 per kg and makes an overall profit of 64%. Then, Amal’s cost price for syrup, in rupees per kg, is:
A) 160
B) 180
C) 220
D) 220
Solution:- [Expected time to be taken: 90 to 120 seconds, Level of Difficulty: Hard]
Let the price of juice be Rs. $x$ per kg.
Since the cost price of syrup is 20% less than the cost price of juice, the cost price of syrup is $0.8x$ per kg.
Total cost price of syrup $= 110 × 0.8x = 88x$
Total cost price of juice $= 120 × x = 120x$
Total cost price $= 88x + 120x = 208x$
Since the overall profit percentage is 64%,
Total profit $= 0.64(208x) = 133.12x$
Profit generated by selling 10 kg of syrup which costs
Rs $0.8x$ per kg at 10% profit $= 0.1 ×10 ×0.8x = 0.8x$
Profit generated on selling 20 kg of juice which costs Rs $x$ per kg at 20% profit $= 0.2 ×20x = 4x$
The remaining profit $(133.12x - (0.8x + 4x) = 128.32x)$ is generated by selling 100 kg of syrup and
100 kg of juice at Rs 308.32 per kg.
The total selling price of 100 kg of syrup and 100 kg of juice is 200 × 308.32 = 2×(30832)
The cost price of 100 kg of syrup $= 0.8x ×100 = 80x$
Cost price of 100 kg of juice = $100x$
Total cost price $= 80x + 100x = 180x$
Profit = Selling price – Cost price
⇒ $128.32x = 2×(30832) - 180x$
⇒ $308.32x = 2×(30832)$
⇒ $x = 200$
Cost price of syrup per kg = 0.8 × (200) = Rs 160
Hence, the correct answer is option (1).
The most important CAT quantitative aptitude topics, along with the CAT quantitative aptitude practice questions, are provided in the table below. The candidates are encouraged to practice CAT quantitative aptitude questions from these topics as they have a high probability of being asked in the CAT examination.
|
Section |
Title |
Download Link |
|
Arithmetic |
Time, Speed and Distance | |
|
Ratio and Proportion | ||
|
Time and Work | ||
|
Percentages | ||
|
Algebra |
Surds and Indices | |
|
Logarithms | ||
|
Linear and Quadratic Equations and Mixtures and Alligations | ||
|
Sequence and Series | ||
|
Geometry |
Triangles | |
|
Circle | ||
|
Modern Maths |
Permutations and Combinations | |
|
Number Systems |
Remainders | |
|
Coordinate Geometry |
How to Prepare for Profit and Loss in the CAT Exam
Here are a few points that can help you solve profit and loss effectively.
1. Learn conversions from percentages to fractions and vice versa.
2. You should learn specific tricks to solve the particular type of question.
3. In the questions of true weight/ false weight, Selling Price has always been calculated on the reading, while Cost Price has always been calculated on actual weight. After that, compare the final selling price and the final cost price to find the profit or loss percentage.
4. Practice all kinds of problems separately.
Time allocation strategy for CAT Quant
1. Identify the questions that take less time.
2. Eliminate the wrong choices by analysing the options.
3. Use Assumptions and approximations while solving the questions.
Best books and resources for Profit & Loss
1. Arun Sharma: A Quantitative Approach for CAT (7th Edition)
2. Quantitative Aptitude for CAT by Nishit K Sinha
CAT 2025 Preparation Resources by Careers360
The candidates can download the various CAT preparation resources designed by Careers360 using the links given below.
|
eBook Title |
Download Links |
|
CAT 2025 Arithmetic Important Concepts and Practice Questions | |
|
CAT 2025 Algebra Important Concepts and Practice Questions | |
|
CAT 2025 Number System - Important Concepts & Practice Questions | |
|
CAT 2025 Exam's High Scoring Chapters and Topics | |
|
CAT Mock Test Series - 20 Sets, Questions with Solutions By Experts | |
|
Mastering CAT Exam: VARC, DILR, and Quant MCQs & Weightages | |
|
CAT 2025 Mastery: Chapter-wise MCQs for Success for VARC, DILR, Quant | |
|
CAT 2025 Quantitative Aptitude Questions with Answers | |
|
CAT 2025 Important Formulas | |
|
Past 10 years CAT Question Papers with Answers | |
|
CAT 2025 Quantitative Aptitude Study Material PDF - Geometry and Mensuration |
Frequently Asked Questions (FAQs)
Q: How should I tackle the questions based on faulty weight?
A:
You can find the formula to solve the questions on faulty weight. But without using a formula, these questions can be handled more effectively.
Assume the purchase rate and selling rate according to the information given in the question.
Multiply the purchase rate by the actual quantity given to the customer to find the CP.
Multiply the selling rate by the reading (quantity for which the customer actually paid) to find the SP.
Now, compare SP and CP to find the desired profit or loss percent.
Q: How to solve the questions like, Selling two items at the same price, one at 25% profit, another at 25% loss, what is the overall gain or loss %?
A:
In this case, one will always incur a loss which is equal to the square of the loss% divided by 100.
Here, loss% = 6.25%.
Q: How can I improve my speed while solving profit and loss questions?
A:
You can work on a few points:
1. Focus on conceptual clarity rather than using formulas.
2. Learn percentage to fraction and fraction to percentage conversion.
3. Do calculations mentally.
Q: Which method should I use to solve the questions: formula, ratio-fraction, or assumption (CP = 100)?
A:
It depends on the question.
If a direct value question is asked, then use the formula.
If percentage values are given in integers, you can use the assumption (CP = 100)
If percentage values are given in decimals, you can use the ratio-fraction method.
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Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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