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CAT Questions | CAT Arithmetic Questions : Percentage Problems

The percentage questions are an integral part of the CAT Questions, XAT Exam, NMAT Exam and various other exams. Across the years it has been recorded that percentage aptitude questions come in many forms both in the quantitative section and the data interpretation and logical reasoning section of CAT questions. Even if percentage problems don’t come directly, the percentage aptitude is mixed with other topics and are asked indirectly. CAT exam aspirants must prepare percentage aptitude tricks thoroughly to get a high percentile in the exam. “Percent” as the word suggests means for every hundred. 

Importance of Percentage concept for CAT/XAT/SNAP


YearNo of QuestionsGood attemptsDifficulty Level


Slot 123Moderate
Slot 231Moderate


Slot 134Easy
Slot 243Moderate


Slot 143Easy
Slot 233Easy



YearNo of QuestionsGood attemptsDifficulty Level


YearNo of QuestionsGood attemptsDifficulty Level


List of Concepts within Percentage

The list of concepts that are covered in the Number System chapter is as follows: –

• Percentages, fractions and ratios

• Base system

• Concept of change of base

• The multiplying factor (MF) – a% increase is 1 + (a/100) and a% decrease is 1 – (a/100).

• Successive percentage changes

for example, A number N undergoes a percentage change of a % and then b %, the net change is:

New number = N × (1 + a/100) × (1 + b/100)

Now, (1 + a/100) × (1 + b/100) = 1 + a/100 + b/100 + ab/10000

If we say that a + b + ab/100 = c, then (1 + a/100) × (1 + b/100) = 1 + c/100

Hence, c is the effective percentage change when a number is changed successively by two percentage changes

• Concept of indexing

• Concept of simple interest- Simple interest is that type of interest which once credited does not earn interest on itself. It remains fixed over time.

The formula to calculate Simple Interest is

SI = {(P x R x T)/ 100}

Where P = Principal (the original loan taken/ deposit)

R = rate of interest for loan/ deposit

T = time period (time duration for which loan is borrowed)

• Concept of compound interest- An amount P is deposited in an account or lent to the borrower that pays compound interest at the rate of R% p.a. Then after n years the deposit or loan will become:


• Concept of interest on interest

• Cost price, selling price, profit, loss, mark up, discount and margin

CAT Quantitative Aptitude questions | CAT Arithmetic : Percentage Problems

1. In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to  (CAT 2020)

A) 59 B) 55 C) 66 D) 62

 In a group 28% are young, 72% are old

In the same group 65% are literates and 35% are illiterates

Young literates = 1/4 (65%) = 16.25%, So remaining 11.75% are young illiterates.

Out of 35% illiterates = 11.75% is young and remaining 23.25% are old illiterates

So, 23.25/35 × 100 ≅ 66

2. The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala’s income goes down by 4% and Bimala’s goes up by 10%, then the percentage by which Kamala’s income would exceed Bimala’s is nearest to- 31, 28, 32, 29 (CAT 2019 slot 1)

Let the income of Amala (A) = 100x , income of Bimala (B) = 100x/1.2 = 83.33 x and

Income of Kamala = 100x/0.8 = 125x

When Kamala’s income goes down by 4% and Bimala’s goes up by 10%,

K’s new income = 125x – 4% of 125x = 120x

B’s new income = 83.33x + 10% of 83.33x = 91.67 x

the percentage by which Kamala’s income would exceed Bimala’s = (120x – 91.67x)/91.67x *100= (28.33/91.67) *100 = 31 (approx) 

3. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at a 5% gain and the book at a 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees? (CAT 2019 slot 1)

Let the CP of pen = p and that of book = b

So as per question 0.15 b – 0.05 p = 7

Or 15b – 5p = 700 ————-1)

Similarly 10b + 5p = 1300 —–2)

Adding both equations 25b = 2000

Or b = 2000/25 = 80

4. A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2: 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was- (CAT 2019 slot 1)

Final interest at the end of the year = 76000,

Interest rate = 76000/1500000 *100 = 76/15 = 5 1/15

Combine interest rate from amount deposited at 4% and 3% interest rate = (4*2 + 3)/(2+1) =11/3 %

Let the amount ratio of amount deposited in fixed deposit and other deposit be x:y so

x/y = ( 76/15 -11/3 )/(6 – 76/15)

x/y = (76-55)/(90 -76) = 19:14

amount deposited in 6% = 19/33 *15 =8.63 lakh = 9 lakh

How to prepare for the concept of Percentage

Level 1

Understand the basic concepts of CAT questions and learn the basic conversions by heart- from percentage chapter to fraction to decimal should be done with perfection (for example 0.5 is equal to 50% which is equal to 1/2). CAT 2021 is a speed test as much as a test to assess the aspirant’s skills. Ample practice needs to be done to do calculations for CAT questions with speed and do calculations mentally as far as possible with percentage tricks. You can refer MBAP CAT E Book (Concept Theory) study material and MBAP Live Lecture Recording (Basic) on basic concept for more clarity. Also, the different tips and tricks should be customized to individual students’ needs as no two students are identical and need their own ways to carry out calculations. At the present level, NCERT books from classes 10th to 12th can be referred to for brushing up the basics and practicing entry-level calculations using MBAP CAT E Book (Practise Questions) and MBAP lecture Assignment. 

Level 2

Moving on to the intermediate level CAT questions, the focus should be on solving the questions correctly. The speed of solving the questions should not be focused on at this stage. An Excel sheet can be maintained to monitor the progress in the questions by the student. The CAT questions where difficulty was faced should be revised after a week again and if the difficulty is faced again, then the concept should be revised. For the intermediate level, material from a coaching center like the MBAP CAT E Book (Practise Questions) and MBAP lecture Assignment can be referred to as it has graded material with sections divided into different levels of difficulty.

Level 3

Moving on to the advanced level, along with accuracy, speed should also be taken into account as it is important for the final CAT questions using MBAP Previous year CAT paper. Mocks should be given at this level. Many mocks should be given in a timed environment and a complete analysis needs to be carried out. A mixture of different levels of difficulty CAT questions should be attempted through section-wise tests with MBAP CAT Advance E books. Attempting too many easy or too many difficult questions is not advised. Taking up a mock test series from a coaching institute will be beneficial. The art of selecting which questions to attempt and which to leave should be instilled at this stage, also which topics should be attempted and which to leave is also identified right now. 

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