# CAT Questions | CAT Arithmetic Questions

###### CAT Quantitative Aptitude | CAT Percentage, Profits, SICI

CAT exam has historically tested Percentages, Profit and Loss and Simple Interest and Compound interest in every edition of the exam. With every passing year, CAT exam has increased the importance of Arithmetic Questions from topics such as Percentages, Profit and Loss, and Simple Interest and Compound interest. CAT exam has started featuring questions that are a combination of multiple ideas in arithmetic. CAT exam will usually contain 4-5 questions from these topics. 2IIMs CAT questions provides enough questions learn, practice and apply the ideas learnt. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Arithmetic: Profit and Loss - Progressions

A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?

1. 24
2. 18
3. 27
4. 32

2. #### CAT Arithmetic: Percentages - Variables

P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take?

1. 10% to 28%
2. 10% to 25%
3. 10% to 37%
4. 10% to 43%

3. #### CAT Arithmetic: Percentages - Mixtures

An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?

1. 30% ≤ x ≤ 40%
2. 32.5% ≤ x ≤ 42%
3. 33.33% ≤ x ≤ 40%
4. 32.25% ≤ x ≤ 40%

4. #### CAT Arithmetic: Percentages - Integers

A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E earns 20% more than A. A, B, C, D, and E earn integer amounts less than Rs. 100. What is the total amount earned by all five of them put together?

1. Rs. 300
2. Rs. 245
3. Rs. 305
4. Rs. 480

5. #### CAT Arithmetic: Percentages - Golden Ratio

A is x% more than B and is x% of sum of A and B. What is the value of x?

1. 50%
2. 62%
3. 75%
4. 37%

6. #### CAT Arithmetic: Percentages - Variables

A, B, C and D share a loot. A gets a% of the total. B gets b% of the remaining (after A has taken his share). C gets c% of the remaining and D gets the rest. D gets a% less than what A gets, B and C get equal amounts. b = 2a.
1. What percentage of what A got did C get?
2. If the total amount is equal to Rs. 1000, what is the difference between what A got and what D got?

1. 160% , A got Rs.40 more than D
2. 80% , A got Rs.20 more than D
3. 175% , A got Rs.50 more than D
4. 150% , A got Rs.35 more than D

7. #### CAT Arithmetic: Percentages - Variables

A is x% less than B, A is y% less than C. C is k% more than B. Express k in terms of x and y.

1. Rs. 2160
2. Rs. 1420
3. Rs. 1580
4. Rs. 2210

14. #### CAT Arithmetic: Percentages - Variables

A is x % more than B. B is y % less than C. If A, B and C are positive and A is greater than C, find the relation between x and y.

1. y (1 - x) < x
2. y (1 - x) > x
3. y (1 + x) < x
4. y (1 + x) > x

15. #### CAT Arithmetic: SICI - Installments

Krishna borrows Rs. 45K from a bank at 10% compound interet. He repays it in three annual installments that are in arithmetic progression. He ends up paying 54K totally. How much did he pay in year 1?

1. Rs. 16,500
2. Rs. 19,500
3. Rs. 21,000
4. Rs. 18,000

16. #### CAT Arithmetic: Compound Interests

On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.

1. Rs. 2,400
2. Rs. 2,800
3. Rs. 2,000
4. Rs. 1,600

17. #### CAT Arithmetic: Simple Interest and Compound Interest

Ram deposits Rs. P with a bank at r% compound interest and sees it reach Rs.16P in 20 years. If he had invested the same amount at r% simple interest for 20 years, what would be the amount?

1. Between Rs. 2P and 2.5P
2. Between Rs. 2.5P and 3P
3. Between 3P and 3.5P
4. Between 3.5P and 4P

18. #### CAT Arithmetic: Simple Interest and Compound Interest

Ram earns an interest of 600 over two years on a simple interest basis. On a compound interest basis, at the same interest rate, he would earn Rs. 630. What is the rate of interest?

1. 5%
2. 20%
3. 30%
4. 10%

19. #### CAT Arithmetic: Profit and Loss - Percentages

Ram sells onions in the streets of Chandni Chowk. Due to recent shortfall in the supply of onions, he doubles his selling price despite the cost price remains same for him due to a fixed price contract. He realizes that his profit have tripled. Find the original profit percent.

1. 200/3%
2. 100%
3. 120%
4. 105∗1/3%

20. #### CAT Arithmetic: Discount Percentage

Given below is a question followed by three statements. Study the statements and decide which of the statement(s) is/are necessary to answer the question. What was the discount percentage given?
I) On selling the table, for Rs 12650, 26.5 %, Profit was earned.
II) If there had been no discount, 30% would have been earned as profit.
III) The Cost price of the table was Rs 10000

1. Only I and II
2. Only II and III
3. Only I and III
4. Any two of the above
5. None of these

21. #### CAT Arithmetic: Total number of students

In a practice paper at 2iim.com, questions were given from 5 topics. Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?

1. 2500
2. 2000
3. 1600
4. 4545

22. #### CAT Arithmetic: Overall Change

Tensile strength of a material A is a multiple of amount of materials a, b, c, d used. If the amount of material of a, b, c, d are changed by +30%, -30%, -25%, +25% respectively, what will be the overall change in tensile strength of A?

1. No Change
2. +14.68%
3. –14.68%
4. Depends on the initial amount of a, b, c, d

23. #### CAT Arithmetic: Number of balls

A bucket has ‘a’ number of small and large balls out of which b% are black. Of the small balls, c% are black and of large balls, d% are black. Find the number of small balls in the bucket.

1. Rs 4,900
2. Rs 5,200
3. Rs 5,000
4. Rs 6,000

25. #### CAT Arithmetic: Percentages - Number of students

In an examination, 35% of students failed in quants and 42% of students failed in verbal while 14% failed in both the topics. If 222 students passed in both the topics, how many students appeared to write the examination?

1. 500
2. 600
3. 700
4. 800

26. #### CAT Arithmetic: Percentage Change

A solid cube made of steel is melted and recast such that its length, breadth and height changes as +10%, +10%, -20%. What is the percentage change in surface area of this cube?

1. No Change
2. +1%
3. +2%
4. -1%

27. #### CAT Arithmetic: Percentages - Elections

In a local election, 2400 people were to vote for Party A or Party B. Party A was bound to win the election. However, on Election Day, one-third of the voters of Party A were kidnapped. Party B was also able to influence the remaining Party A voters and thus double the strength of its voters. In this way, Party A lost by a majority which was half of that by which it would have won had the elections been fair. How many people finally voted for Party A and Party B?

1. 600(A), 1200(B)
2. 300(A), 600(B)
3. 450(A), 900(B)
4. 600(A), 900(B)

28. #### CAT Arithmetic: Percentages - Discount

Recently a band was to perform in India. However, there was widespread criticism of the high cost of its tickets so the organizers decided to offer the following discounts:

The tickets were originally priced at Rs 25,000/ticket. Any additional tickets (above the lot sizes) were billed at the original price.A college group wants to buy 13 tickets, what is the minimum average ticket price they would need to pay (approx.)?

1. 23,375
2. 23,367
3. 23,380
4. 23,400

29. #### CAT Arithmetic: Percentages - Discount

Recently a band was to perform in India. However, there was widespread criticism of the high cost of its tickets so the organizers decided to offer the following discounts:

The tickets were originally priced at Rs 25,000/ticket. Any additional tickets (above the lot sizes) were billed at the original price.A college group wants to buy 36 tickets, what would be the minimum price (approx) per ticket if the group wanted to buy 36 tickets?

1. Rs.23,300
2. Rs.23,250
3. Rs.23,166.67
4. Rs.23,500

30. #### CAT Arithmetic: Mixtures

In an ice-cream factory, 30% of total Vanilla-flavored ice-cream produced is mixed with 40% of total Banana-flavored ice-cream produced, in a ratio of 1:1. Find the overall percentage of ice-cream produced which is mixed with each other. (Ice-creams of only these 2 flavors are produced in the factory)

1. 17.14%
2. 34.28%
3. 35%

31. #### CAT Arithmetic: Percentages - Travel Expenses

Hari prepares a budget to visit London. However, he spends 12% of his budget on the first 10% days of his travel when he stays in the city. He knows that he has to spend another 35% of days in city itself, after which he would travel to the country side. What should be the minimum decrease in spending in country side as a percentage of his spending in city so as to complete his travel on the initial budget itself?

1. 33.33%
2. 30.3%
3. 25%
4. 32.23%

32. #### CAT Arithmetic: Work Efficiency

In a field, two workers are planting trees. After sometime, a third worker is added and the number of trees planted becomes half as large. How many trees can the second worker plant as a percentage of the number of trees planted by first worker if it is given that efficiency of second worker is 1/3 of 1st and 3rd worker combined.

1. 65%
2. 60%
3. 70%
4. 75%

33. #### CAT Arithmetic: Percentages - Burger Competition

A, B and C participated in a burger eating competition. A beat C by 18 burgers. A also beat B by eating 50% more burger than B. Also B had eaten 5 percentage points more burger than C. Find the overall number of burgers that were eaten.

1. 90 burgers
2. 81 burgers
3. 72 burgers
4. 100 burgers

34. ##### The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

IPMAT Rohtak Sample Paper Mock
IPMAT Indore Sample Paper Mock

Please note that the explanation button will take you to the IPMAT solution page.

35. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,SICI

Veena has to pay Rs. 2460 to Sita, 5 Months later at 6% SI per annum, and Gita has to pay Sita same amount at 7.5% SI per annum after certain months. If both took the same amount of loan from Sita then Gita paid loan after how many months?

1. 3 Months
2. 4 Months
3. 6 Months
4. 12 Months

36. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Percentages

If x% of y is equal to z then what percentage of z is x?

2. #### CAT 2017 Question Paper Slot 1 - Percentages

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 59500, then Ravi's total monthly savings (in Rs) is: (TITA)

3. #### CAT 2017 Question Paper Slot 1 - Profit & Loss

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

1. Give a discount of 5% on retail price
2. Give a discount of 2% on retail price
3. Increase the retail price by 2%
4. Sell at retail price

4. #### CAT 2017 Question Paper Slot 1 - Percentages

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:

1. 35
2. 50
3. 60
4. 65

5. #### CAT 2017 Question Paper Slot 1 - Profit & Loss

In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is:

1. 6%
2. 8%
3. 10%
4. 12%

6. #### CAT 2017 Question Paper Slot 1 - Profit & Loss

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

1. 30%
2. 25%
3. 24%
4. 28%

7. #### CAT 2017 Question Paper Slot 2 - Percentages

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

1. 13600
2. 13000
3. 13400
4. 14000

8. #### CAT 2017 Question Paper Slot 2 - Profit & Loss

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

1. 1500
2. 2000
3. 2500
4. 3000

9. #### CAT 2017 Question Paper Slot 2 - Profit & Loss

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

1. 50
2. 30
3. 25
4. 45

10. #### CAT 2017 Question Paper Slot 2 - Percentages

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

1. 16
2. 13
3. 10
4. 7

11. #### CAT 2018 Question Paper Slot 1 - SI & CI

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The ï¬?rst instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is:[TITA]

12. #### CAT 2018 Question Paper Slot 1 - Percentages

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?

1. N ≤ 200
2. 243 ≤ N ≤ 252
3. N ≥ 253
4. 201 ≤ N ≤ 242

13. #### CAT 2018 Question Paper Slot 2 - SI & CI

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankitâs dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y. (TITA)

14. #### CAT 2019 Question Paper Slot 1 - Percentages

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 [TITA]

15. #### CAT 2019 Question Paper Slot 1 - Percentages

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

1. 75
2. 80
3. 60
4. 70

16. #### CAT 2019 Question Paper Slot 1 - Simple interest

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 [TITA]

17. #### CAT 2019 Question Paper Slot 1 - Profit & Loss

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?

1. 80
2. 85
3. 100
4. 95

18. #### CAT 2019 Question Paper Slot 1 - Percentages

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

1. 28
2. 29
3. 31
4. 32

19. #### CAT 2019 Question Paper Slot 2 - Percentages

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?

1. 6600
2. 6160
3. 6000
4. 5500

20. #### CAT 2019 Question Paper Slot 2 - Percentages

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]

21. #### CAT 2019 Question Paper Slot 2 - Profit & loss

Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was

1. 2000
2. 6000
3. 8000
4. 4000

22. #### CAT 2019 Question Paper Slot 2 - Simple interest & Compound interest

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is [TITA]

23. #### CAT 2019 Question Paper Slot 2 - Profit & loss

A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x -y) / p equals

1. 1
2. 1.2
3. 0.7
4. 0.50

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