Profit & Loss in CAT 2025: Only 3 Formulas Needed for All Variations

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

In 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

1. 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.

2. 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.

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.

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.

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.

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.