Let’s explore the Percentage Questions for the competitive exam because they make a solid presence in the Quantitative Aptitude section in the CAT exam. In Percentage, questions, aspirants have to learn the formula to score well in the CAT exam. The difficulty level of the Percentage, questions can be easy to moderate.
What is Percentage Questions for CAT?
Percentage questions in the CAT examination have an integral role in Quantitative Ability —one of three sections of the competitive exam. These questions test candidates’ ability to work with percentages in various problems & situation. For example, finding out the percentage increase in the price of an item or finding out by what percentage a population has decreased.
Importance of Percentage Questions in the CAT Exam
Percentage questions importance in the CAT exam can’t be left unnoticed, especially within the Quantitative Ability section. Here’s why they are crucial:
1. Fundamental Concept: Percentages is a very fundamental math concept on which many other concepts, like profit and loss, simple and compound interest, data interpretation, and even algebra depends. If one has a good grasp of percentages, many other concepts become very easy to manage.
2. High Frequency: Percentage-based questions are very frequent in the CAT examination. Because of the versatility, it can get embedded in different problem types and thus becomes a recurring feature across question types.
3. Real-life Application: Percentages are very much related to real-life scenarios, such as calculating discounts, interest rates, increase in population, and data trends. This makes these questions quite practical and relevant.
4. Efficiency at Problem-Solving: A good knowledge of percentages hugely enhances speed and accuracy in solving a problem. Most of the complex questions in the CAT examination can easily be simplified by bringing them down to percentage-related calculations.
5. Data Interpretation: In the DI section, percentage calculations often become an intrinsic part of the interpretation of charts, tables, and graphs. The correct percentage calculations may at times turn out to be the key to the right answers in DI sets.
Solving Percentage Questions for CAT
- Determine the reference value to which the percentage is applied.
- Convert percentage to fraction or vice versa for easier calculations.
- Based on the problem, form an equation using the percentage formula.
- Perform the necessary arithmetic to find the missing value.
- Cross-check the problem to ensure accuracy.
Tips to improve Percentage Questions for CAT?
- Understanding that percentile ranks are calculated and their significance.
- Practice solving problems within time constraints similar to those of the CAT exam and Focus on improving both speed and accuracy in calculations.
- Regularly take mock tests to practice exam conditions and evaluate your preparation level.
Percentage Questions Tricks for the CAT Exam
- Understand that percentages represent parts per hundred. For example, 25% means 25 out of 100.
- Develop mental calculation skills to compute percentages swiftly.
- Utilize ratios to solve percentage problems, especially those involving comparisons or distributions of quantities.
Percentage Questions Formulae for the CAT Exam
- Percentage of a number = ( Part/whole) * 100
- Finding a number of its percentage = Part = (Percentage / 100) * Whole
- Finding what percentage One number is another = Percentage = (Part/whole) * 100
Common Question Types of Percentage in CAT
Percentage is a fundamental concept in mathematics and forms a crucial part of the Quantitative Aptitude section in CAT. Here are the common question types you can expect:
- Finding the percentage of a number: Direct application of the percentage formula.
- Finding the number when a percentage is given: Inverting the percentage formula.
- Percentage increase or decrease: Calculating the change in value as a percentage of the original value.
- Successive percentage changes: Understanding the combined effect of multiple percentage changes.
- Profit and loss: Such concepts ask you to weight up profit or loss percentage based on cost price and selling price.
- Discount: Determining the selling price after applying a discount percentage.
Advanced Percentage Concepts
- Change of base: With this we mean converting percentages from one base to another.
- Fractions and percentages: such concepts require you converting between fractions and percentages.
- Simple Interest and Compound Interest: It involves calculation of interest amounts based on principal, rate, and time.
- Ratio and Proportion: It is mostly about converting ratios to percentages and vice versa.
- Mixtures and Allegations: Finding the ratio of quantities to achieve a desired percentage.
- Calculations involving percentages: Determining percentage increases, decreases, and comparisons.
Percentage Practice Questions for CAT
Q 1. Ashish started a business with an initial investment of 500000. In the first year, he incurred a loss of 4%. However, during the second year, he earned a profit of 5% which in the third year rose to 10%. Calculate his net profit for the entire period of three
years.
(a) 48800
(b) 54400
(c) 55000
(d) None of these
Level: Easy
Answer: Option C
Q2. The present value of an optical instrument is 20000.If its value will depreciate 5% in the first year, 4% in the second year and 2% in the third year, what will be its value after 3 years?
(a) 16534.5
(b) 16756.5
(c) 17556.8
(d) 17875.2
Level: Difficult
Answer: Option A
Q 3. The population of a variety of tiny bush in an experimental field increased by 10% in the first year, increased by 8% in the second year but decreased by 10% in the third year. If the present number of bushes in the experimental field is 26730, then the number of bushes in the beginning was
(a) 25000
(b) 27000
(c) 28000
(d) 24600
Level: Moderate
Answer: Option D
Q 4. The production of a company has ups and downs every year. The production increases for two consecutive years consistently by 15% and in the third year it decreases by 10%. Again in the next two years it increases by 15% each year and decreases by 10% in the third year. If we start counting from the year 2008, approximately what will be the effect on production of the company in 2012?
(a) 27% increase
(b) 32% increase
(c) 37% increase
(d) 42% increase
(e) 52% increase
Level: Moderate
Answer: Option D
Q 5. The present population of a country estimated to be 10 crores is expected to increase to 13.31 crores during the next three years. The uniform rate of growth is
(a) 8%
(b) 10%
(c) 12.7%
(d) 15%
Level: Difficult
Answer: Option C
What are the must-do Percentage questions for the CAT exam?
Q 6. Peter earned 40% more money than Albert. Albert earned 20% less than Michael. Peter earned more than Michael by
(a) 10%
(b) 12%
(c) 20%
(d) 25%
Level: Difficult
Answer: Option D
Q 7. A large watermelon weighs 20 kg with 96% of its weight being water. It is allowed to stand in the sun and some of the water evaporates so that only 95% of its weight is water. Its reduced weight will be
(a) 16 kg
(b) 16.5 kg
(c) 17 kg
(d) 18 kg
Level: Moderate
Answer: Option C
Q 8. Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of dry grapes is 250 kg what was its total weight when it was fresh?
(a) 1000 kg
(b) 1100 kg
(c) 1125 kg
(d) 1225 kg
Level: Easy
Answer: Option B
Q 9. An alloy of gold and silver weighs 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?
(a) 30 g
(b) 40 g
(c) 50 g
(d) 60 g
Level: Easy
Answer: Option B
Q 10. In a mixture of milk and water, the proportion of water by weight was 75%. If in the 60 gms mixture 15 gm of water was added, what would be the percentage of water?
(a) 75%
(b) 88%
(c) 90%
(d) 100%
(e) None of these
Level: Difficult
Answer: Option B
What are the most important Percentage questions for the CAT 2024 exam?
Q 11. The population of the colony was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been co stant over the years and has been compounding annually?
(a) 6000
(b) 6400
(c) 7200
(d) 9600
Level: Moderate
Answer: Option A
Q 12. The value of a flat worth 500000 is depreciating at the rate of 10% p.a. In how many years will its value be reduced to 364500?
(a) 3 years
(b) 4 years
(c) 5 years
(d) 6 years
Level: Difficult
Answer: Option C
Q 13. After 30 kg of water had been evaporated from a solution of salt and water, which had 15% salt, the remaining solution had 20% salt. The weight of the original solution was
(a) 80 kg
(b) 90 kg
(c) 120 kg
(d) 135 kg
Level: Moderate
Answer: Option C
Q 14. 85% and 92% alcoholic solutions are mixed to get 35 litres of an 89% alcoholic solution. How many litres of each solution are there in the new mixture?
(a) 10 of the first and 25 of the second
(b) 20 of the first and 15 of the second
(c) 15 of the first and 20 of the second
(d) 12 of the first and 23 of the second
Level: Easy
Answer: Option C
Q 15. How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?
(a) 20
(b) 24
(c) 30
(d) 32
Level: Difficult
Answer: Option C
Find some previous year Percentage questions from CAT 2023 exam?
Q 16. A 27 quartz capacity car radiator is filled with 18% alcohol solution. How many quartz be drained and then be replaced by a 90% alcohol solution for resulting solution to contain 42% alcohol?
(a) 7 quartz
(b) 9 quartz
(c) 11 quartz
(d) 14 quartz
Level: Moderate
Answer: Option C
Q 17. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than that I had paid. What percent of the total amount paid by me was paid for the pen?
(a) 37.5%
(b) 50%
(c) 62.5%
(d) None of these
Level: Moderate
Answer: Option A
Q 18. The majority against a certain motion is equal to 8% of the total number of voting. If 14 of those who voted against it had voted for it, the motion would have been carried by 4 votes. Find the number of votes for and against the motion.
(a) 112, 126
(b) 138, 162
(c) 128, 144
(d) 148, 172
Level: Easy
Answer: Option B
Q 19. The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly polls and the Praja Party lost by a majority twice as large as that by which it had won the previous Assembly polls. If a total 2,60,000 people voted each time how many voted for the Praja Party in the previous Assembly polls?
(a) 110000
(b) 120000
(c) 140000
(d) 150000
Level: Difficult
Answer: Option C
Q 20. State Electricity Board gives 15% discount on electric bills if it is paid before due date. One person gets 54 as discount. The amount of actual bill was:
(a) 362
(b) 359
(c) 360
(d) 361
Level: Moderate
Answer: Option C
Q 21. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?
(a) 32 kg
(b) 40 kg
(c) 52 kg
(d) 80 kg
Level: Easy
Mistakes Others Make That You Can Avoid
- Misinterpreting or neglecting the base value can lead to incorrect percentage calculations.
- Incorrectly converting percentages to fractions or decimals can lead to calculation errors.
- Some percentage problems can be solved with simple logic or shortcuts, but candidates often complicate them.
- Rounding off too early or incorrectly can distort final answers.
- Ignoring units or the context of the problem can lead to answers that don’t make sense.
Solutions on How to Avoid These Mistakes
- Now, let's say a product is originally priced at Rs. 200. It is offered with a 15% discount, and you have to come up with the sales price. Making a common mistake of using the sale price directly (e.g., Rs. 200-15% of Rs. 200) will result in an incorrect calculation.
- Be careful in converting percentages into fractions or decimals. For example, you must convert 25% correctly to 0.25 or 1/4 and then apply.
- You can calculate many common percentages in your head. For instance, 10% of 150 is 0.10×150 =15. Easy Right? Similarly, consider 50% of 120 as 0.5×120=60.
- Round off the numbers only after the calculations have been done. This will avoid errors. Suppose you got 25.50, it is the nearest whole number to 26. Now, you had rounded off 25.50 to 26 before you did your complete calculation, your answer would still be incorrect.
Answer: Option A
What are some other important CAT Arithmetic Questions with Solutions?
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