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18 Percentages PYQ (Solutions)

Master Percentages for CAT 2026 with practice questions and detailed explanations

CAT 2025

Percentages form the basis of many arithmetic problems (profit, interest, data interpretation, etc.). Direct percentage calculation questions or comparisons appear often.

  • CAT 2017–2019 always included a couple of percentage-based questions (either standalone or embedded in other topics).
  • In CAT 2020, percentages were part of the “Averages, Ratios, Percentage…” bucket, contributing up to 4 questions in a slot.
  • CAT 2021 had percentages integrated into several arithmetic questions (the group “Averages, Ratios, Percentage, Mixtures” was about 4–5 questions per slot).

Because percentages are fundamental, multiple questions every year rely on this concept.

Expected Weightage:
You can expect 2–4 explicit percentage questions each year (percentage increase/decrease, comparisons, fraction–percent conversions). Additionally, strong percentage skills are crucial for DI sets and other QA topics across 2017–2024.

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Weightage Over Past Years

YearQ.NODifficulty Level
20243Medium
20232Medium
20211Hard
20203Medium
20195Medium
20181Medium
20173Medium

CAT 2024 Percentages questions

Question 1

Slot-1

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

14.84
12.75
13.26
15.18

Question 2

Slot-2

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

Question 3

Slot-3

After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

27.5
30
25
20

CAT 2023 Percentages questions

Question 1

Slot-3

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

Question 2

Slot-3

The population of a town in 2020 was 100000 . The population decreased by y% from the year 2020 to 2021 , and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between x and y is 10 , then the lowest possible population of the town in 2021 was

74000
75000
72000
73000

CAT 2021 Percentages questions

Question 1

Slot-3

The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is

68.75
68.50
68.25
69.25

CAT 2020 Percentages questions

Question 1

Slot-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

59
62
66
55

Question 2

Slot-2

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent 450 on rice in April, then how much did he spend on wheat in May?

590
580
560
570

Question 3

Slot-3

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

399
439
357
417

CAT 2019 Percentages questions

Question 1

Slot-1

In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys, pass an examination, the percentage of the girls who do not pass is

Question 2

Slot-1

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

28
29
31
32

Question 3

Slot-1

Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is

75
80
60
70

Question 4

Slot-2

In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

6600
6160
6000
5500

Question 5

Slot-2

In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was [TITA]

CAT 2018 Percentages questions

Question 1

Slot-1

In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

N ≤ 200
243 ≤ N ≤ 252
N ≥ 253
201 ≤ N ≤ 242

CAT 2017 Percentages questions

Question 1

Slot-1

The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:

35
50
60
65

Question 2

Slot-2

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

16
13
10
7

Question 3

Slot-2

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

13600
13000
13400
14000

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