25+ Profit & Loss Questions for CAT with SOLUTIONS

Profit & Loss is the most important part of Quantitative Aptitude. Questions from Profit & Loss will help in other MBA entrance exams such as CAT, NMAT, MAT and more challenging aspirants with the Profit & Loss concepts. Learning all the formulas is essential for scoring well in this section, where questions range from easy to moderate in difficulty level.

Profit is the financial gain and loss is the expenditure which exceeds revenues. The Profit & Loss report shows how much money a business spends and earns over a while. The four main terms in Profit & Loss are Profit, Loss, Cost Price, and Selling Price.

Importance of Profit & Loss in the CAT Exam

• Repetitive Topic: Profit & Loss questions seen in the past few years in the Quantitative Aptitude section. So, it's important to go through it thoroughly.

• Interconnected Concepts: Many Profit & Loss Questions contain ratio, percentage, and proportional reasoning. These topics are fundamental in data interpretation and logical reasoning in the CAT exam.

• Speed: Practice Regularly Profit & Loss Questions helps in quick calculation solving and understanding.

• How it is Relevant in MBA: Profit & Loss is the topic that will help in the MBA curriculum. As it helps in the understanding of profitability, cost management, and decision-making.

Steps to Solving Profit & Loss Problems

1. Understanding of the Basic Concepts:  The Most basic thing to keep in mind for the Profit and Loss question is that prices of various items throughout purchase and sale. Prices are Cost Prices, Selling Prices, and Marked Prices which are abbreviated as C.P., S.P., and M.P..

2. Identify the Given Information: Start Reading the question carefully and pick the relevant data. Do not get confused about Cost Prices Selling Prices and Marked Prices . 

3. Determine What Needs to be Found: Based on the given information in the question Know what they are asking to find and solve the question accordingly.

4. Use the Appropriate Formula: Select the correct formula to answer the questions and choose the right mathematical method to solve it.

5. Solve Step-by-Step: Break - down the question into smaller sections to solve it more easily.

6. Double-Check Your Calculations: Review the Calculations once after solving the question to be sure there is no mistake

7. Practice with Different Types of Problems: It will help in your Problem Solving Skills and boost the confidence

Tips and Tricks for Quick Calculations

• Memorize basic formulas for quick calculations.
• Calculate Percentages based on C.P. (Cost Price)
• Practice solving maximum problems to enhance your calculation.
• Be organized with your answers. Write neatly so that you don't get confused with the numbers and formulas.
• Understand fundamental Profit & Loss concepts and Formulas

• Cost Price: The price at which product is purchased, is called its cost price also known as C.P.
• Selling Price: The price at which product is sold, is called its selling price also known as S.P.
• Profit or Gain: If S.P. is greater than C.P., the seller is having a profit or gain
• Loss: If S.P. (Selling Price) is less than C.P (Cost Price)., the seller is said to face a loss

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3. Loss or gain is always reckoned on C.P.
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Profit Formula: If the selling price of the product is more than cost price the question is of profit. In simple words If the product is sold at a higher price than the cost of the product. Then we can find that it is a profit question

Loss Formula: If the cost price of the product is more than the selling price the question is of Loss. In simple words If the product is sold at a lower price than the cost of the product. Then we can find that the question is of loss

Profit & Loss Percentage Formula: In some Questions, it is asked to convert the profit or loss in the percentage. It is used to find up whether the company is having profit or enduring loss in a better way. It also helps in comparing two quantities

Basic Profit & Loss Questions

• Basic Profit and Loss Questions: Basic Profit & Loss calculations based on S.P. and C.P.

• (SP) or (CP) Calculation: The question is about Finding CP (Cost Price) or SP (Selling Price) when other along with profit or loss percentage is given.

• Finding Profit/Loss Percentage: Calculation of profit or loss percentage when CP (Cost Price) and SP (Selling Price) are known.

• Successive Transactions: Calculating where involving multiple transactions where an item is bought and sold more than once.

Advanced Profit & Loss Questions

• Discounts and Marked Prices: Questions that involve the calculation of discount percentage, marked price, and selling price after discount.

• Percentage Increase/Decrease: Questions focusing on the increase or decrease in price and its impact on profit/loss.

Mistakes others make that you can Avoid

• Ignoring Fixed and Variable Costs
• Forgetting to Include All Costs
• Refrain from getting confused in C.P. and S.P.
• Misinterpreting Percentage calculations
• Pay serious attention to words like "Discounts", "Percentage", "Price", "S.P." and "C.P." etc.
• Misapplying the formula for P&L

Solutions on How to Avoid These Mistakes 

• Classify costs accurately: Fixed costs remain constant regardless of production levels,  while variables fluctuate with production.

• Mention CP and SP very carefully: Always double-check the figures for CP and SP. Ensure you use the correct values for calculations, including any discounts or markups.

• Double-check the mentioned Costs: Include all discounts and returns in your calculations. Adjust the selling price accordingly to get an accurate profit or loss figure.

• Ensure all relevant costs are included: This provides a true picture of expenses and profitability.

• Understand and Apply: Understand the difference and apply the correct formula. Markup is calculated on cost price, while margin is calculated on selling price.

• Consider the time period: Consider the time period for which you are calculating profit and loss. Ensure that all costs and revenues within that period are accounted for.

Q1. Anil bought a second-hand bike for some price from Ankit. Anil spent 5000 on repairs and then sold the bike at 25 percent profit to Sushil. Sushil found that the tyres of the bike were very old so he spent 5000 in replacing the tyres. He then sold the bike at a price which was 20,000 more then the price at which Ankit sold the bike to Anil. If Sushil earned a profit of 16.67 percent then find the price at which Anil sold the bike.

Level: Moderate

Q2. Rohit buys 12 toys and labels each with the same selling price. Rohit sells 8 toys initially at a 20% discount on the labeled price. Then Rohit sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, Rohit gets a total of Rs 2112 and makes a 10% profit. With no discounts, his percentage of profit would have been
A. 50
B. 60
C. 54
D. 55

Level: Easy

Q3. A milkman has 100L of milk with him. He bought this 100L for 10000 Rs. He sells 20L of it at 80Rs per liter and replaces the sold milk by water. He then again sells 20L of the mixture at 85 Rs per liter and replaces it with water. He then sells 25L of the mixture at 90 Rs per liter and replaces it with water. He then finally sells 25L at 95 Rs per liter. What is his overall profit/loss in these transactions, assume water comes free of cost? (if you feel he had a loss of X Rs the put -X as the answer and if you feel he had an overall profit of X Rs then put X as the answer

Level: Difficult

Q4. A certain amount is given at compound interest and the amount increased by 27% between the 2nd year and 4th year. After how many years does the amount double itself? A. 8 years B. 7 years C. 6 years D. Can't be determined

Level: Easy

Q5. Money invested by Veeru Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. After how many years Veeru's investment, will their balances, i.e., principal plus accumulated interest, be equal?

Level: Easy

Q6. A loan amount of Rs. 7200 was repaid in two equal half-yearly installments. If the rate of compound interest is 50% p.a compounded semi-annually, what is the amount paid in each installment?

Level: Difficult

Q7. Radhika earns a salary of 10000x, where x is an integer. Her salary is increased by x%, then the salary becomes 10000p, where p is a perfect square. Then the salary of Radhika after the increase is
A. Rs. 2250000
B. Rs. 1960000
C. Rs. 1440000
D. Rs. 2560000

Level: Easy

Q8. Ritika invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Level: Easy

Q9. Ashuman had an initial capital of Rs.20,000. Out of this, he invests Rs.8,000 at 5.5% in bank A,₹5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Ashuman combined annual interest income from these investments is equal to 5% of the initial capital. If Ashuman had invested his entire initial capital in bank C alone, then his annual interest income, in rupees, would have been A. 900 B. 700 C. 1000 D. 800

Level: Moderate

Q10. Kavita borrows Rs. X from Fatima at 8% annual interest. She then adds Rs. Y of her own money and lends Rs. X+Y to Shaurya at 10% annual interest. At the end of the year, after returning Fatima’s dues, the net interest retained by Kavita is the same as that accrued to Fatima. On the other hand, had Kavita lent Rs. X+2Y to Shaurya at 10%, then the net interest retained by her would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y. _______

Level: Difficult

Q11. Ramesh deposited a sum ₹A (A > 1000) in a bank, which offers a simple interest of 12.5% p.a on deposits, for a period of two years. At the end of two years, Ramesh withdrew the total amount and lent it to Suresh at x% p.a., compounded annually. If the interest due for the first year on Suresh’s loan was ₹2000 and Suresh owes a total of ₹14400 to Ramesh at the end of the second year, what is the value of A?
A. 8000
B. 10000
C. 5000
D. 12500

Level: Easy

Q12. If the difference between the total compound interest and the total simple interest accrued on a certain sum at a certain rate of interest at the end of two years is 6.25% of the principal, find the number of years in which the sum will quadruple under simple interest.
A. 12
B. 16
C. 20
D. 24

Level: Moderate

Q13. If the compound interest accrued on a certain sum, at 11% p.a, for two years is ₹1064.8 more than the simple interest accrued on the same sum, at the same rate and for the same period, what is the sum?
A. ₹9,680
B. ₹8,800
C. ₹80,000
D. ₹88,000

Level: Easy

Q14. In an examination, The total score is N while the pass mark is 45% of N. Sachin obtains 36 marks but falls short of the pass mark by 68%. Which of the following statements may be true?
A. N ≤ 200
B. 243 ≤ N ≤ 252
C. N ≥ 253
D. 201 ≤ N ≤ 242

Level: ModerateShow Answer & Explanation

Q15.Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment what is his overall profit percentage?
A. 15% 
B. 20%
C. 25% 
D. 40%

Level: Easy

Q16.A shopkeeper offers 2.5% discount on cash purchases. What cash amount would Rohan pay for a cycle, the marked price of which is ` 650? 
A. 633.25 
B. 633.75
C. 634 
D. 635

Level: Easy

Q17.If a company sells a car with a marked price of 2,72,000 and gives a discount of 4% on 2,00,000 and 2.5% on the remaining amount of 72,000, then the actual price charged by the company for the car is
A. 2,50,000 
B. 2,55,000
C. 2,60,100 
D. 2,62,200

Level: Difficult

Q18.Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was 1400, at what price did she purchase the briefcase?
A. 980 
B. 1008
C. 1056 
D. 1120
E. None of these

Level: Easy

Q19.A dealer buys an article marked at 25000 with 20% and 5% off. He spends 1000 on its repairs and sells it for 25000. What is his gain or loss percent?

A. Loss of 25% 
B. Gain of 25%
C. Loss of 10% 
D. Gain of 10%

Level: Moderate

Q20.Raman bought a camera and paid 20% less than its original price. He sold it at 40% profit on the price he had paid. The percentage of profit earned by Raman on the original price was 
A. 12 
B. 15
C. 22 
D. 32

Level: Difficult

Q21.A shopkeeper gives 3 consecutive discounts of 10%, 15% and 15% after which he sells his goods at a percentage profit of 30.05 percent on the cost price. Find the value of the percentage profit that the shopkeeper would have earned if he had given discounts of 10% and 15% only. 
A. 53% 
B. 62.5%
C. 68.6% 
D. 72.5%

Level: Easy

Q22.By selling an umbrella for ` 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is 
A. 7 
B. 7.5
C. 8 
D. 9

Level: Moderate

Q23.The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%. 
A. 37.5% 
B. 48%
C. 50.5% 
D. 52%

Level: Difficult

Q24. There was a bag which have a total of 120 coins in denominations of Rs 1, Rs 2 and Rs 5. The value of Rs 2 coins is at most 40% of the total value of the coins. The value of Rs 5 coins in the bag is atmost 25% of the total value of the coins in the bag. If there are at most 70 Rs 1 coins in the bag, how many Rs 2 coins are there in the bag?
A. 38
B. 42
C. 40
D. Cannot be determined

Level: Easy

Q25. Ritik scores 40% in an exam and after review, even Ritik's score is increased by 50%, he fails by 35 marks. If his post-review score is increased by 20%, he will have 7 marks more than the passing score. The percentage score needed for passing the examination is
A. 75
B. 80
C. 60
D. 70

Level: Easy

Q26. Income of Karan is 20% more than that of Rahul and 20% less than that of Manas. If Manas's income goes down by 4% and Rahul's goes up by 10%, then the percentage by which Manas's income would exceed Rahul's is nearest to
A. 28
B. 29
C. 31
D. 32

Level: Difficult