Previous Year CAT Questions for Arithmetic

1. CAT 2024 QA Slot 1 | Arithmetic - Percentage CAT Question

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

(a)
12.75
(b)
14.84
(c)
15.18
(d)
13.26

2. CAT 2024 QA Slot 2 | Arithmetic - Percentage CAT Question

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

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3. CAT 2023 QA Slot 1 | Arithmetic - Percentage CAT Question

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

(a)
26%
(b)
25%
(c)
30%
(d)
28%

4. CAT 2023 QA Slot 3 | Arithmetic - Percentage CAT Question

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

(a)
73000
(b)
72000
(c)
75000
(d)
74000

5. CAT 2023 QA Slot 3 | Arithmetic - Percentage CAT Question

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

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6. CAT 2022 QA Slot 2 | Arithmetic - Percentage CAT Question

In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was:

(a)
60288
(b)
50240
(c)
40192
(d)
62800

Answer: Option D

Video Explanation

Text Explanation :

Let the total number of registered voters be 100x.
Number of votes casted = 80x

Votes for Candidate 1 = 30% of 80x = 24x
∴ Remaining three candidates will recieve = 80x - 24x = 56x votes.

Remaining 3 candidates get votes in the ratio of 1 : 2 : 3 of the remaining 56x votes.
⇒ Votes of Candidate 2 = $\frac{1}{6}$ × 56x = $\frac{28 x}{3}$
⇒ Votes of Candidate 3 = $\frac{2}{6}$ × 56x = $\frac{56 x}{3}$
⇒ Votes of Candidate 4 = $\frac{3}{6}$ × 56x = 28x

Highest number of votes is received by Candidate 4 while second highest is by Candidate 1.
⇒ 28x – 24x = 2512
⇒ x = 2512/4 = 628

∴ total number of registered votes = 100x = 62800

Hence, option (d).

7. CAT 2021 QA Slot 1 | Arithmetic - Percentage CAT Question

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

(a)
127
(b)
135
(c)
144
(d)
124

Answer: Option A

Video Explanation

Text Explanation :

Let the weight and price of small box is ‘w’ and ‘p’ respectively.
∴ Selling price per gram for small box = p/w

Now, selling price per gram for large box = 0.88p/w

Also, selling price for the whole box = 2p.

⇒ Weight of the large box = $\frac{2 p}{0.88 p / w}$ = $\frac{2 w}{0.88}$ = $\frac{25 w}{11}$

∴ Required percentage = $\frac{\frac{25}{11} w - w}{w}$ × 100 = 14/11 × 100 ≈ 127%

Hence, option (a).

8. CAT 2021 QA Slot 2 | Arithmetic - Percentage CAT Question

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

(a)
10
(b)
15
(c)
5
(d)
70

Answer: Option A

Video Explanation

Text Explanation :

Let the loss incurred by Raj in first year = P%

∴ Amount remaining after 1st year = 10,000 $(1 - \frac{P}{100})$ > 5,000 …(1)

Now the percentage growth next year = 5P%

∴ Amount after 2 years = 10,000 $(1 - \frac{P}{100})$ $(1 + \frac{5 P}{100})$

Overall growth after 2 years is 35%, hence amount after 2 years should be 10,000 × 1.35

⇒ 10,000 $(1 - \frac{P}{100})$ $(1 + \frac{5 P}{100})$ = 10,000 × 1.35

⇒ 10000 – 5P² + 400P = 13500

⇒ 5P² - 400P + 3500 = 0

⇒ P² – 80P + 700 = 0

⇒ P = 10% or 70%.

P cannot be 70% since amount remaining after 1st year has to be greater than 5000 [from (1)]

∴ P = 10%

Hence, option (a).

9. CAT 2021 QA Slot 3 | Arithmetic - Percentage CAT Question

In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be

(a)
78
(b)
84
(c)
80
(d)
86

10. CAT 2021 QA Slot 3 | Arithmetic - Percentage CAT Question

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

(a)
68.50
(b)
69.25
(c)
68.75
(d)
68.25

Answer: Option C

Video Explanation

Text Explanation :

Let the male and female population be ‘m’ and ‘f’ in 1970.

Using alligation

$\frac{m}{f}$ = $\frac{25 - 20}{40 - 25}$ = $\frac{1}{3}$

∴ f = 3m

Total population in 1970 = f + m = 4m

⇒ Number of females in 1980 = 1.2f = 3.6m and number of males in 1980 = 1.4m

Population in 1990
Number of females = 1.25 × 3.6m = 4.5m
Number of males = ½ × 4.5m = 2.25m
Total population = 4.5m + 2.25m = 6.75m

⇒ Total population increases from 4m in 1970 to 6.75m in 1990.

∴ Percentage increase = 2.75m/4m×100 = 68.75%.

Alternately,
Let the number of males and females in 1970 be 'm' and 'f' respectively.

∴ In 1980, number of males = 1.4m, females = 1.2f and total population = 1.25(m + f)
⇒ 1.4m + 1.2f = 1.25(m + f)
⇒ 0.15m = 0.05f
⇒ m : f = 1 : 3

∴ In 1990, number of females = 1.25 × 1.2f = 1.5f, number of males = 1/2 × 1.5f = 0.75f
∴ Total population in 1990 = 1.5f + 0.75f = 2.25f

Also, total population in 1970 = m + f = f + f/3 = 4f/3

⇒ Required percentage = $(\frac{2.25 f - 4 f / 3}{4 f / 3})$ × 100% = $\frac{11}{16}$ × 100% = 68.75%

Hence, option (c).

11. CAT 2020 QA Slot 1 | Arithmetic - Percentage CAT Question

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

(a)
55
(b)
66
(c)
59
(d)
62

12. CAT 2020 QA Slot 2 | Arithmetic - Percentage CAT Question

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?

(a)
Rs. 580
(b)
Rs. 560
(c)
Rs. 590
(d)
Rs. 570

13. CAT 2020 QA Slot 3 | Arithmetic - Percentage CAT Question

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

(a)
399
(b)
439
(c)
417
(d)
357

14. CAT 2019 QA Slot 1 | Arithmetic - Percentage CAT Question

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

(a)
60
(b)
80
(c)
70
(d)
75

15. CAT 2019 QA Slot 1 | Arithmetic - Percentage CAT Question

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

(a)
31
(b)
29
(c)
28
(d)
32

Answer: Option A

Video Explanation

Text Explanation :

Let incomes of Amala, Bimala and Kamala be a, b and k respectively.

∴ a = $\frac{6}{5}$ × b = $\frac{4}{5}$ × k.

∴ $\frac{k}{b}$ = $\frac{3}{2}$

Let Kamala's income be 300 and Bimala's income be 200.

∴ Kamala's new income = 300 × 0.96 = 288 and Bimla's new income = 200 × 1.1 = 220.

∴ Required percentage = $(\frac{288 - 220}{220})$ × 100 = $(\frac{68}{220})$ × 100 = 30.9 ≈ 31%.

Hence, option (a).

16. CAT 2019 QA Slot 1 | Arithmetic - Percentage CAT Question

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

(a)
95
(b)
85
(c)
100
(d)
80

17. CAT 2019 QA Slot 1 | Arithmetic - Percentage CAT Question

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

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18. CAT 2019 QA Slot 2 | Arithmetic - Percentage CAT Question

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?

(a)
6600
(b)
6160
(c)
6000
(d)
5500

Answer: Option A

Video Explanation

Text Explanation :

In 2010 : Total books = 11500

Let the number of fiction books be f, non-fiction books will be (11500 - f)

In 2015 : Total books = 12760

Increase in total number of books = 12760 - 11500 = 1260

Fiction books increase by 10%, non-fiction books increase by 12%.

Hence, f × $\frac{10}{100}$ + (11500 - f) × $\frac{12}{100}$ = 1260

10f + 12 × 11500 – 12f = 126000

x = 6000 books

So, Fiction books in 2015, 6000 + 600 = 6600 books

Hence, option (a).

19. CAT 2019 QA Slot 2 | Arithmetic - Percentage CAT Question

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

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20. CAT 2019 QA Slot 2 | Arithmetic - Percentage CAT Question

The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6 : 5 : 7 in 2010, and in the ratio 3 : 4 : 3 in 2015. If Ramesh's salary increased by 25% during 2010-2015, then the percentage increase in Rajesh's salary during this period is closest to

(a)
7
(b)
8
(c)
9
(d)
10

Answer: Option A

Video Explanation

Text Explanation :

The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6 : 5 : 7 in 2010

In 2010, let salary of Ramesh = 6x, Ganesh = 5x & Rajesh = 7x

In 2015, their salaries are in the ratio 3 : 4 : 3 respectively.

In 2015, let salary of Ramesh = 3y, Ganesh = 4y & Rajesh = 3y

Now, Ramesh’s salary increased by 25%

Hence, 3y = 5/4 × 6x

⇒ y = 2.5x

∴ Rajesh’s salary in 2015 = 3y = 3 × 2.5x = 7.5x

Percentage increase in Rajesh's salary during 2010 - 2015 = $\frac{7.5 - 7}{7}$ × 100% ≈ 7.

Hence, option (a).

21. CAT 2018 QA Slot 1 | Arithmetic - Percentage CAT Question

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?

(a)
N ≤ 200
(b)
201 ≤ N ≤ 242
(c)
243 ≤ N ≤ 252
(d)
N ≥ 253

Answer: Option C

Video Explanation

Text Explanation :

Passing marks = 45% of N

As 36 marks are short of the pass marks by 68%, it means the cadidate got (100 - 68 = ) 32% of the passing marks.

⇒ 36 = 32% of 45% of N

∴ 36 = 0.32 × 0.45 × N

∴ N = $\frac{36}{0.32 \times 0.45}$ = 250

Hence, option (c).

22. CAT 2017 QA Slot 1 | Arithmetic - Percentage CAT Question

Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

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23. CAT 2017 QA Slot 1 | Arithmetic - Percentage CAT Question

Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59,500, then Ravi's total monthly savings (in Rs) is:

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24. CAT 2017 QA Slot 1 | Arithmetic - Percentage CAT Question

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:

(a)
35
(b)
50
(c)
60
(d)
65

Answer: Option D

Video Explanation

Text Explanation :

Let the number of boys appearing for the admission test be b.
Number of girs appearing for the admission test = 2b.

Total boys who got admission = 45% of b = 0.45b
Total girls who got admission = 30% of 2b = 0.6b
Total students who got admission = 0.45b + 0.6b = 1.05b

∴ Percentage of candidates who get admission = $\frac{1.05 b}{2 b + b} \times 100 %$ = 35%

∴ 65% of the candidates do not get admission.

Hence, option (d).

25. CAT 2017 QA Slot 2 | Arithmetic - Percentage CAT Question

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

(a)
13600
(b)
13000
(c)
13400
(d)
14000

Arithmetic - Percentage - Previous Year CAT/MBA Questions

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