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CAT is one of the toughest exams for MBA aspirants in India. Among the various topics in Quant, percentage questions hold a lot of importance. Percentage calculations are essential to solve many problems like profit and loss, discounts, data interpretation etc. This post will cover the basic percentage formulas, previous year CAT percentage questions and 10 most important percentage questions with solutions to help you crack this section.
Importance of Percentage Questions in CAT
Percentage questions are basic in CAT because they are the foundation of many complex problems. They test a candidate’s ability to interpret data, understand relationships and do quick calculations. Master of percentage calculations helps in solving direct percentage questions and also improves problem solving speed and accuracy in related topics like profit and loss, simple and compound interest, data interpretation.
Percentages is one of the very important topic for CAT. Every year about 2-3 questions of moderate difficulty keep appearing. Checking CAT Previous Papers will give you a fare idea of the type of questions being asked across years. Learning formulae, reciprocals and all the necessary concepts will help you have a strong foundation. To get a decent understanding of this topic, practice standard questions from Percentages and also take CAT mock tests as many as you can, which will help you get diverse experience.
Percentage Important Formulas
Understanding and memorizing key percentage formulas is essential for tackling CAT percentage questions efficiently. Here are some of the most important formulas:
- Basic Percentage Formula:
Percentage = (Part / Whole) * 100 - Percentage Change:
Percentage Change = ((New Value - Old Value) / Old Value) * 100 - Percentage Increase:
New Value = Old Value * (1 + Percentage Increase / 100) - Percentage Decrease:
New Value = Old Value * (1 - Percentage Decrease / 100) - Successive Percentage Change:
Effective Percentage Change = (x + y + (xy / 100)) % - Profit Percentage:
Profit % = (Profit / Cost Price) * 100 - Loss Percentage:
Loss % = (Loss / Cost Price) * 100 - Discount Percentage:
Discount % = (Discount / Marked Price) * 100 - Percentage of a Percentage:
Percentage of a Percentage = (a / 100) * (b / 100) * 100 - Population Change Formula:
Final Population = Initial Population * (1 + Rate / 100)^n
wherenis the number of periods.
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CAT Percentage Previous Year Questions and Answers
Type I
1.If the price of a commodity increases by 25% and the consumption decreases by 20%, what will be the effect on the expenditure?
Answer: To find the effect on expenditure, we use the successive percentage change formula: Effective Percentage Change = 25 + (-20) + (25 * -20) / 100. This equals 5 – 5 = 0%, meaning the expenditure remains unchanged.
2. A student scored 60% in an exam and failed by 20 marks. If the pass percentage is 70%, what are the maximum marks?
Answer: Let the maximum marks be x. The student scored 0.60x and needed 0.70x to pass, so:
0.70x - 0.60x = 20
0.10x = 20
x = 200
Thus, the maximum marks are 200.
3.The population of a town increased by 10% in the first year and decreased by 20% in the second year. What is the net percentage change in the population after two years?
Answer: Using the successive percentage change formula: Effective Percentage Change = 10 + (-20) + (10 * -20) / 100. This equals -10 – 2 = -12%, so the net change is a 12% decrease.
4.A man spends 75% of his income. If his income increases by 20% and his expenditure increases by 10%, what is the percentage increase in his savings?
Answer: Let the original income be 100, then expenditure is 75, and savings is 25.
New income = 120
New expenditure = 75 * 1.10 = 82.5
New savings = 120 - 82.5 = 37.5
Percentage Increase in Savings = ((37.5 – 25) / 25) * 100 = 50%
5. A shopkeeper marks his goods 20% above the cost price and allows a discount of 10% on the marked price. What is his gain percent?
Answer: Let the cost price be 100. The marked price is 120. After a 10% discount, the selling price is 120 * 0.90 = 108. Thus, the gain percent is:
(108 - 100) / 100 * 100 = 8%
Type II
6.The price of sugar is increased by 25%. By what percentage must a housewife reduce the consumption of sugar so as not to increase the expenditure?
Answer: Let the original price be 100 and the new price be 125. To maintain the same expenditure, the consumption must reduce by:
(125 - 100) / 125 * 100 = 20%
7.A student scored 20% and failed by 30 marks. Another student scored 32% marks and got 42 marks more than the passing marks. What is the passing percentage?
Answer: Let the maximum marks be x. Passing marks = 20% of x + 30 and 32% of x - 42:
0.32x - 0.20x = 72
0.12x = 72
x = 600
Marks = 20% of 600 + 30 = 120 + 30 = 150.
Passing percentage = (150 / 600) * 100 = 25%
8. If the population of a town increases by 20% annually, what will be the population after 2 years if the current population is 10,000?
Answer: After the first year, the population is 10,000 * 1.20 = 12,000. After the second year:
12,000 * 1.20 = 14,400
The population will be 14,400.
9. A person spends 60% of his income and saves the rest. If his income increases by 25% and his expenditure increases by 15%, what is the percentage increase in his savings?
Answer: Let the original income be 100, then expenditure is 60 and savings is 40. New income = 125, new expenditure = 60 * 1.15 = 69:
New savings = 125 - 69 = 56
Percentage increase in savings = ((56 – 40) / 40) * 100 = 40%
Type III
10. The price of a laptop is increased by 15% and then decreased by 15%. What is the net percentage change in the price of the laptop?
Answer: Using the successive percentage change formula: Effective Percentage Change = 15 + (-15) + (15 * -15) / 100. This equals 0 – 2.25 = -2.25%, so the net change is a 2.25% decrease.
11. The salary of a person was first increased by 10% and thereafter increased by 20%. By what percentage does his salary increase overall?
Answer: Using the successive percentage change formula: Effective Percentage Change = 10 + 20 + (10 * 20) / 100. This equals 30 + 2 = 32%, so the salary increased by 32% overall.
12. A product costs $1000 initially. If the price is increased by 10% every year, what will be the price after 2 years?
Answer: After the first year, the price is 1000 * 1.10 = 1100. After the second year:
1100 * 1.10 = 1210
The price will be $1210.
13. A person’s salary is increased by 25% and then decreased by 20%. What is the net percentage change in his salary?
Answer: Using the successive percentage change formula: Effective Percentage Change = 25 + (-20) + (25 * -20) / 100. This equals 5 – 5 = 0%, so there is no net change in the salary.
14. If a man’s income is increased by 20% and his expenditure is increased by 10%, then what is the percentage increase in his savings if initially he saves 25% of his income?
Answer: Let the original income be 100, then expenditure is 75 and savings is 25. New income = 120, new expenditure = 75 * 1.10 = 82.5:
New savings = 120 - 82.5 = 37.5
Percentage increase in savings = ((37.5 – 25) / 25) * 100 = 50%
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CAT Expected Percentage Questions and Answers
Type I
1. The price of sugar is increased by 25%. By what percentage must a housewife reduce the consumption of sugar so as not to increase the expenditure?
Options: A) 10%
B) 20%
C) 25%
D) 30%
Answer: B) 20%
2. A student scored 20% and failed by 30 marks. Another student scored 32% marks and got 42 marks more than the passing marks. What is the passing percentage?
Options: A) 20%
B) 24%
C) 28%
D) 30%
Answer: C) 28%
3. If the population of a town increases by 20% annually, what will be the population after 2 years if the current population is 10,000?
Options: A) 12,000
B) 14,400
C) 15,000
D) 16,000
Answer: B) 14,400
4. A person spends 60% of his income and saves the rest. If his income increases by 25% and his expenditure increases by 15%, what is the percentage increase in his savings?
Options: A) 25%
B) 40%
C) 50%
D) 75%
Answer: C) 50%
5. The price of a laptop is increased by 15% and then decreased by 15%. What is the net percentage change in the price of the laptop?
Options: A) No change
B) 2.25% increase
C) 2.25% decrease
D) 0.75% decrease
Answer: C) 2.25% decrease
6. A company gives a 10% discount on the marked price and still makes a profit of 20%. If the cost price is $200, what is the marked price?
Options: A) $220
B) $240
C) $250
D) $300
Answer: D) $300
Type II
7. A man spends 80% of his income. His income increases by 25% and his expenditure increases by 15%. Find the percentage increase in his savings.
Options: A) 40%
B) 50%
C) 60%
D) 70%
Answer: D) 70%
8. A product costs $120 after a 20% discount. What was the original price?
Options: A) $140
B) $150
C) $160
D) $180
Answer: C) $150
9. If a number is increased by 25% and then decreased by 20%, what is the net change in the number?
Options: A) 0%
B) 2.5% increase
C) 4% increase
D) 10% increase
Answer: B) 2.5% increase
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Conclusion
Mastering percentage calculations is essential for excelling in the CAT exam. Knowing the formulas and practicing with previous years questions will give you a lot of confidence and score. The questions above along with the solutions are a complete guide to solve percentage questions.
Remember consistent practice and clear concepts are the key. Practice, stay focused and you will see improvement in your problem solving and overall score.
Frequently Asked Questions
How many questions are asked from percentage topic in CAT?
CAT Percentage Questions are an important topic for the candidates aspiring to take the CAT as every year, out of 9-10 Arithmetic questions, 1-2 questions are from percentages.
How can I improve my skills in percentage questions?
To improve your skills, practice regularly with a variety of percentage questions, understand key concepts, and use effective problem-solving strategies. Focus on common types of percentage problems and review your mistakes to learn from them.
What are some common types of percentage questions asked in CAT?
Common types include basic percentage calculations, percentage increase/decrease, profit and loss percentage, and percentage changes over multiple periods.
Where can I find resources to practice percentage questions for CAT?
You can find practice questions in CAT preparation books, online CAT prep websites, mock tests, and specialized courses such as Entri’s CAT coaching course.
Can I use a calculator for percentage questions in CAT?
No, the use of a physical calculator is not allowed in the CAT exam. However, an on-screen calculator is provided for basic calculations. It’s best to practice mental math and quick calculation techniques.
Can I appear for CAT more than once?
Yes, you can appear for CAT multiple times. There is no limit to the number of times you can take the CAT exam.
