Percentage Questions for CAT - Download Free Question & Answer PDF

What are Percentage Questions for CAT?

The term "percent" is derived from the Latin “per centum”, meaning "hundred" or "by the hundred". The percentage is a fraction or number expressed as a part of 100. The symbol of percentage is (%). The value of percent is computed by multiplying the numeric value of the ratio by 100. 

For example, to find 30 apples as a percentage of 1200 apples, one first computes the ratio of 30/1200 and then multiplies by 100 to obtain 0.25 %. Candidates preparing for the CAT Exam must understand the concept of percentage in a comprehensive manner to ensure that questions asked to lead to positive marking. 

Types of Percentage Questions for CAT

The percentage is a part of Arithmetic and comes under the Quantitative Ability section of the CAT exam. There are various types of Percentage Questions for CAT which if practiced well by the CAT aspirants will help them to score well. 

Some of the types are mentioned below:

a) Percentage increase /decrease

b) Change of base

c) Applications based on Percentage

Formulas for Percentage Questions for CAT

Percentage Questions for CAT consists of a lot of formulas that the candidates need to learn in order to solve questions based on percentage easily. Solving questions using formulas will help the candidates to solve Percentage Questions for CAT quickly and accurately. Given below are some basic formulas for Percentage Questions for CAT.

Percentage to Fraction 

20% = 20 /100 = 1/5 

35% = 35 /100 = 7/20 

Fraction to Percentage 

1/4 = 1/4 × 100 = 25% 7/8 = 7/8 × 100 = 87.5%

Percentage increase and decrease: 

Fraction for Percentage Increase 

Increase of 20% 

20% = 1/5 

∴ New value = (1+ 1/5 ) × Original Value = 6/5 × Original Value Fraction for Percentage Decrease 

Decrease of 14.28% 14.28% = 1/7 

∴ New value = (1 – 1/7 ) × Original Value = 6/7 × Original Value 

Percentage Offset:

If the price of petrol is increased by 14.28%. By how much should you reduce your consumption to keep the expenses constant? 

Let Price = 1, Consumption = 1 ⟹ Expenses = 1 × 1 = 1 P × C = P′ × C′ ⟹ 1 × 1 = 8 7 × C′ ∴ C′ = 7/8 

Consumption to be reduced = (1 – 7/8 ) = 12.5% 

Percentage change: 

If A is 20% less than B, then B is ______% more than A. 

A = 4/5 

B ⟹ B = 5/4 A

 ∴ B is (1 + 1/4 ) × A 

∴ B is 1/4 more than A. 

∴ B is 25% more than A. 

Successive percentage change:

If a change of a% is followed by another change of b%, then Net Change = a% + b% + ( ab 100)%

Sample Percentage Questions for CAT

Listed below are some of the sample questions based on percentage. The candidates can go through the Percentage Questions for CAT given below in order to ace the quantitative aptitude section of the CAT Exam. The Percentage Questions for CAT given below will provide the candidates with an overview of the type of questions that are asked on this topic. 

You must also go through CAT percentage questions from the previous year to gain a better understanding of the kind of questions asked. Download CAT Question Paper to practice, 

Question 1: 64% of a bigger number is 6 more than 75% of a smaller number. The bigger number is 140 more than the smaller one. What is the sum of both numbers?

Answer: 1660

Explanation: Let the smaller number be x, then

The bigger number = (x + 140)

According to the question

(x + 140) × 64% – x × 75% = 6

0.64x + 89.6 – 0.75x = 6

⇒ x = 760

Required sum = Smaller number + Bigger number = x + (x + 140) = 760 + 900 = 1660

Question 2: If the length of a rectangle is increased by 16% and its breadth is decreased by 25%, find the percentage decrease in the area of the rectangle.

 Answer: 13%

Explanation: Let the original length and breadth of the rectangle be 100 units and 40 units respectively.

Question 3: The total salary of A and B is Rs 60,000. If the salary of A increases by 8% and the salary of B increase by 6%, then their total salary would increase to Rs 64,100. Find the salary of B

Answer: Rs 35000

Question 4: The number of seats in a stadium is decreased by 15% and also the price of the ticket is increased by 20%. What is the effect on the revenue collected?

 Answer: 2% increase

Explanation: Let the number of seats in the stadium initially be 100.

Let the price of each ticket initially be Rs. 10.

Initial revenue of the stadium = 100 × 10 = Rs. 1000

New number of seats in the stadium = 85% of 100 = 85

New price of each ticket = 120% of 10 = Rs. 12

New revenue of the stadium = 85 × 12 = Rs. 1020

Increase in revenue of stadium = 1020 – 1000 = Rs. 20

Percent increase in revenue of the stadium = (20/1000) × 100 = 2%

Question 5: A man spent 40% of his monthly income on food items. Of the remaining amount, he spent 80% on E M.I. Now he saves 5/6 of the remaining amount and then he saves 78,600 yearly. Find the monthly income of a man.

 Answer: 65500

Percentage Questions for CAT PDF

As Percentage Questions for CAT appear in the exam regularly, it is advised that candidates practice as many questions as possible. Solving the past year's papers and attempting mock tests will help the candidate to understand the different kinds of questions that can be asked on this topic. Candidates can download the Percentage Questions for CAT PDF given below

☛ Percentage Questions for CAT - Download PDF 

How to Solve Percentage Questions for CAT?

Solving Percentage Questions for CAT will help the candidates not only ace the Quantitative Ability section of the CAT exam but also the Data Interpretation and Logical Reasoning section. Following is given the tips and tricks to solve percentage questions for CAT:

•  The Percentage Questions for CAT involve certain formulas and shortcut tricks which if followed thoroughly will help the candidates to solve questions easily. 
• The candidates should practice CAT Mock Test and previous year's question papers on percentages to ace the quantitative aptitude section of the CAT exam.
• It is advised to learn multiplication tables, square roots, and cube roots up to 20. This will help the candidates to solve percentage questions for CAT easily.

Best Books for Percentage Questions for CAT

The candidates often get confused about which books they should refer to for preparing Percentage Questions for CAT. It is advisable that the candidates should always refer to the books and study materials of famous authors/publishers. The aspirants must choose the books containing all the topics under the Quantitative Ability section of the CAT exam. Given below are some of the best CAT Books for Percentage Questions for CAT:

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