300+ Most Important Arithmetic Questions for CAT
Percentage
Percentage is arguably the most important topic in Arithmetic for CAT 2026, directly influencing problems in Profit & Loss, Simple & Compound Interest, and Data Interpretation. Practice exam-oriented CAT arithmetic important questions covering percentage change, successive percentage, and application-driven problems based on recent CAT patterns. These questions are built around repeated CAT concepts and are designed to maximize scoring accuracy.
Arithmetic
Q1. At a textile factory, a new embroidering machine is installed. The cost of the machine depreciates by Rs.1.44 lakh in the second year and by Rs.1.296 lakh in the third year. If the rate of depreciation was constant, what was the initial cost (in Rs. lakh) of the machine?
15.6
16
17.2
18
Q2. Each vendor P, Q, R and S has a box of 800 apples. P sold 10% less number of apples than Q. Q sold 25% more number of apples than R, while R sold 20% less number of apples than S. If P sold 540 apples, find the percentage of apples sold by S.
Q3. In a donation drive, 605 toys were distributed equally among children in such a way that the number of toys received by each child is 20% of total number of children. How many toys did each child got?
Q4. In a school library, there are only fiction and non-fiction books. The number of fiction books is 50% more than the number of non-fiction books. If 60% of the fiction books and 40% of the non-fiction books are borrowed, there are 624 books left in the library. Determine the total number of fiction and non-fiction books originally present.
Q5. A trader mixed two varieties of rice, one costing Rs.96 per kg and the other Rs.112 per kg. He sells 750 g packs of this mixed variety at Rs.105 and gets 40% profit. What is the percentage of dearer rice in the mixed variety?
15%
20%
18%
25%
Q6. In an election survey, 80% of total voters took part, of which 50% claimed to vote for candidate A, 10% are uncertain and rest claimed to vote for B. If all of them voted according to their commitments on the day of election and those who were not part of survey, voted to A and B in ratio of 3: 2. All the people who were uncertain in survey, voted to A and B in the ratio of 1: 4 in election. If A won by 648 votes, then find total number of votes in election.
Q7. In a class, 60% of the students passed the mathematics exam, and the rest failed. Among the students who passed, the highest score achieved was 98, and the lowest score was 40. Among the students who failed, the highest score achieved was 35, and the lowest score was 12. What is the possible range of average score for the entire class?
29 to 74
29 to 72
28 to 72
28 to 73
Q8. A bottle without its lid weighs 12% of its weight when bottle is completely filled with a particular liquid. After adding the lid to the bottle, the weight of the fully filled bottle increases by 2%. If the weight of a partly filled bottle is 1/3 of the completely filled bottle with lid attached, then what fraction of the liquid in the bottle is utilized?
5/22
17/44
17/50
3/22
Q9. In 2019, Company B’s revenue was twice that of Company A. In 2020, A’s revenue rose by 30%, while B’s revenue fell by 20%. In 2021, A’s revenue fell by 15%, while B’s revenue increased by 40%. If the total revenue of both companies combined in 2021 was Rs. 13.38 crores, find their total revenue (in Rs. crores) in 2019.
Q10. Shilpa wrote a book of poems consisting of 40 pages, with each page containing 64 lines and 75 characters per line. If the number of lines is reduced to 50 but the number of characters is increased to 80 per line, what is the percentage change in the number of pages? (Assume the number of pages is a whole number.)
20% increase
18% decrease
15% increase
10% decrease
Q11. A solid metallic cube is melted to form six solid cubes whose volumes are in the ratio 1: 1: 1: 8: 8: 8. What is the percentage by which the sum of the surface areas of these six cubes exceeds the surface area of the original cube?
33.33%
55.56%
77.78%
66.67%
Q12. Ajay participates in a competition consisting of three rounds – I, II and III. Each round was worth a certain number of points, and the total possible score for the competition was 300 points. If Ajay scored 25% of his total points in round I, 35% in round II, and the 52 points in round III, then how much more points did Ajay score in round II than in round I?
Less than 12
Less than 14
Less than 11
More than 13
Q13. Manu earns ₹ 28000 per month at the start of the year, and wants to save an average of ₹ 5000 per month during this year. In the first three months, his monthly expense was ₹ 24500, and he foresees that, from April onwards, his monthly expense will increase to ₹ 29500. By what percentage should his monthly earnings grow if he wishes to meet his yearly savings target?
20
23.33
26.67
25
Q14. Due to excess supply, the price of mangoes reduced by 25%. As a result, Tina could purchase 400 gm extra mangoes with the fixed budget she allotted for mangoes. What was the quantity (in grams) of mangoes that Tina had initially planned to purchase?
Q15. Among all the students of a school, 30% belong to ‘A’ House, 20% belong to ‘B’ House, 12.5% belong to ‘C’ House, and the rest belong to ‘D’ House. A single student cannot belong to more than one House. Among the students in the school 15% of A, 10% of B, 20% of C and 12% of D can speak in English. What percentage of English-speaking students in the school belong to ‘D’ House?
22 2/9%
27 3/11%
33 1/3%
37 3/7%
Q16. A cricket ball weighs only 25% of a football. A tennis ball and a cricket ball together weigh 40% of the weight of a football and a tennis ball together. What is the weight of a tennis ball as a percentage of the weight of a football?
Q17. Amit saves a certain amount from his salary after taking care of the household expenses. Every month, out of his savings, he deposits 25% in a recurring bank deposit, gives 33 1/3% of the remaining amount to his mother and he equally divides the remaining amount among his two sisters for their pocket money. If the total monthly amount distributed by him among his family members (his mother and sisters) is Rs. 3000, then the amount (in Rs.) he deposits in his recurring bank deposit account in one year is:
1000
4000
6000
12000
Q18. In a locality, over a period of 5 years, the total income of the households increased by 35% and the per capita income increased by 25% during the same time. The percentage by which the population of the locality increased during the same period is:
12
10
8
6
Q19. A trader buys potatoes and onions in equal quantities every month. He had to spend Rs. 3000 extra this month as the prices of potatoes and onions increased by 25% and 20% respectively. If the trader used to buy potatoes worth Rs. 8000 every month before the price increase, then the amount he had to spend on buying onions this month, in Rs, is:
4500
5000
5500
6000
Q20. In a garden, 59% of the trees are coconut trees and the rest are mango trees. The number of coconut trees exceeds that of mango trees by 180. If 54% trees, including 245 mango trees, in the garden are older than 10 years, then the percentage of coconut trees, which are ten years or less older, is:
Q21. Sumit expected that his annual electricity consumption (in units) for the year 2023 will be in the ratio of 3: 7: 6: 4 in the first, second, third and the fourth quarter respectively, and accordingly he allotted Rs. 14000 for the annual electricity bill. The actual bills for the first three quarters deviated from his expectations by +10%, +5%, and –4%, respectively. By what percentage should Sumit reduce his electricity consumption in the fourth quarter to meet the allotted annual budget assuming that electricity bill is directly proportional to units consumed?
10.25
12.67
14.5
18.33
Q22. In a 10th standard state board examination, 5% of registered students did not appear for the examination. Among the students who appeared for the examination, 8% could not pass the examination. The ratio of students who passed in first division, second division and p-division (students can pass in these 3 divisions only) is 5: 3: 2. How many students appeared for the board examination if the difference between the number of students who passed in first and p-division is 2622?
10000
11000
9500
11400
Q23. Anil spent 16.67% of his income on rent, 25% of the remaining on food, 60% of then remaining on education. If he is still able to save Rs. 4500 per month, then find his monthly income (in Rs.).
16000
18000
19000
21000
Q24. Neha starts playing a game with some amount. The amount gets increased by some
percentage in the first hour of the game but in the second hour of the game, it was decreased
by the same percentage. At the end of the second hour, she had Rs. 5,040. Similarly, on
increasing and decreasing in the same pattern, also with the same percentage, at the end of
the fourth hour, that amount became Rs. 4,961.25. Following the same pattern, the amount
she had (in nearest integer) at the end of the fifth hour was:
Rs.5,278
Rs.5,581
Rs.5,349
Rs.5,287
Q25. Amit’s present age in years is 75% less than that of Chandan’s. In another few years, Amit’s age will be one-third of Chandan’s. By what percentage will Chandan’s age increase during this period?
10%
20%
12.5%
25%
Q26. In an election, there were four candidates. Exactly a fifth of the registered voters did not cast their votes. One of the candidates received votes from 30% of the total registered voters while the other three candidates received the remaining votes actually cast in the proportion 5: 4: 3. If the winner of the election beat the runner-up by a margin of 2222 votes, then the number of registered voters was:
22220
23230
32320
24240
Q27. A box contains small cubes made of either only wood or only metal. Some cubes are of red colour and the rest are of green colour. The number of red cubes is three times that of green cubes. Among the red cubes, 44% are made of metal and among the green cubes, 48% are made of metal. What percentages of cubes are made up of wood?
52
50
45
55
Q28. In an election, 3/7th of the voters promised to vote Rachit and the rest promised to vote Mohit. 5% of the voters who had promised to vote Rachit changed their minds and voted for Mohit. P% of the voters who had promised to vote Mohit changed their minds and voted for Rachit. The difference between their votes was 10% of the total votes. The value of P can be:
10
15
20
25
Q29. A scientist has two varieties of bacteria for research – Alpha and Beta. The population of Alpha at any point of time is 20% less than what it was exactly 1 hour before. However, the population of Beta at any point of time is 10% less than what it was exactly 1 hour before. It is found that from the starting point of simultaneous acquisition of the colonies of these two different bacteria, the population of the two colonies becomes equal after 4 hours. What was the initial population of bacteria type Beta (in million) if the initial population of bacteria type Alpha was 19683 million?
21228
11288
12288
12828
Q30. The speed of a conveyor belt in an assembly line is controlled using a digital control device. The speed of the conveyor belt at the beginning of the day remains 1200 items per hour. After the lapse of every hour, the speed is reduced by a fixed percentage. The speed of the belt becomes 768 items per hour after two such reductions. At the end of the 3rd hour of the operation the speed of the belt is increased to the value which is equal to the reduced speed it had at the end of the first hour of its operation. What is the value (in items per hour) of the increased speed of the belt after the completion of its 3rd hour of the operation?
Q31. The cost of two types of Balls – A and B – are equal. The shopkeeper increases the price of ball A and Ball B by 10% and 8% respectively. How much more a customer has to pay now to purchase a ball of each variety?
8%
9%
7.5%
10%
32. In a group of 500 people, 60% are women and 40% are men. Of the women, 40% are under 30 years old, and of the men, 50% are under 30 years old. If 40% of people under 30 years old prefer coffee, then what percentage of the group under 30 years old prefer coffee?
20.5%
19%
19.4%
17.6%
Q33. In a class, there are students belonging to three different streams A, B and C. On the day the movie Bahubali was released exactly 35% of A, 68% of B and 76% of C were absent. What is the minimum possible number of students who were present in the class?
27
54
81
74
Q34. Onkar owns a press and has several typists working under him. Some are males and some are females. He finds that 7 males and 5 females type the same number of pages in 10 hours as 2 males and 10 females in 11 hours. The efficiency of a male typist is what percentage more or less than a female typist?
10% more
20% less
25% more
20% more
Q35. Rashi always buys either blue or red hair clips. She discarded some clips and went shopping to buy new hair clips. The number of blue hair clips increased by 28% while the number of red hair clips decreased by 28%. The ratio of the two types of hair clips was exactly reversed. By what percentage did the total amount of hair clips change?
4%
5%
8%
12%
Q36. In an Institute, students can study Languages, Ethics, and Philosophy. Among the students who study a language 35% of them study English. 13% of all the students in the institute study a language other than English. No student studies more than one language. What percentage of the students do not study Languages?
Q37. Out of 40% of the total number of matches, a badminton player has won 8 matches and lost 4 of them. If it’s true that no match can end in a tie, what is the maximum number of matches he can lose and still win more than 60% of the total number of matches?
Q38. In a science fair competition, there are three categories: Experiment, Presentation, and Research, with weightages 25%, 30%, and 45% respectively. The passing percentage for the competition is 75%. If a participant scores 60% of the maximum marks in the Presentation category and 80% of the maximum marks in the Research category, what minimum percentage does the participant need to score in the Experiment category to pass the competition?
84%
96%
100%
90%
Q39. There was a fundraising effort for a party being organized by Ravi. 60% of the participants contributed 80% of the funds. The average contribution of all the people who attended is Rs. 150. What is the average contribution (in Rs.) of the remaining 40% of the people?
Q40. A language school has 2000 students. Between 85% and 90% of the students of this school study German, between 35% and 45% of the students of that school study Korean, and each student of this school studies at least one of the two subjects. What is the difference between the minimum and maximum possible number of students who study both German and Korean?
496
299
298
296
Q41. In a competitive examination, Jatin scored 88% and Surya scored 72%. Prem scored 64 marks less than Jatin and Prem’s score was more than that of Surya by 36 marks. Vijay’s score was 225 marks and the passing percentage was 40% of the total marks. Vijay must have:
Failed by 40 marks
Passed by 30 marks
Failed by 25 marks
Passed by 20 marks
