🎉Ace the Final Stretch with our Last Mile Excellence – Your Ultimate CAT 2024 Boost!

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.

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
Choice C
27
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%
Choice C
10% to 37%
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%
Choice D
32.25% ≤ x ≤ 40%
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
Choice C
Rs. 305
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%
Choice B
62%
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
Choice A
160% , A got Rs.40 more than D
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. \\frac{(y - x)100}{100 - y}\\)
2. \\frac{(y + x)100}{100 - y}\\)
3. \\frac{(y - x)100}{100 - x}\\)
4. \\frac{(y - x)100}{100 + y}\\)
Choice A
\\frac{(y - x)100}{100 - y}\\)
CAT Arithmetic: Percentages - Classroom

In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?
1. 25%
2. 33.33%
3. 40%
4. 20%
Choice D
20%
CAT Arithmetic: Percentages - Classroom

Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
1. 33.33%
2. 40%
3. 25%
4. 60%
Choice B
40%
CAT Arithmetic: Profit and Loss - Merchants

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.
1. 25%
2. 12.5%
3. 37.5%
4. 40%
Choice A
25%
CAT Arithmetic: Percentages - Golden Ratio

a is x % of b, b is x% more than a. Find x.
1. 50%
2. 62%
3. 75%
4. 37%
Choice B
62%
CAT Arithmetic: Percentages - Two digit number

A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.
1. 45
2. 54
3. 63
4. 72
Choice A
45
CAT Arithmetic: Profit and Loss - Maximum

A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
1. Rs. 2160
2. Rs. 1420
3. Rs. 1580
4. Rs. 2210
Choice C
Rs. 1580
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 (100 - x) < 100x
2. y (100 - x) > 100x
3. y (100 + x) < 100x
4. y (100 + x) > 100x
Choice C
y (100 + x) < 100x
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
Choice B
Rs. 19,500
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
Choice C
Rs. 2,000
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
Choice D
Between 3.5P and 4P
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%
Choice D
10%
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%
Choice B
100%
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
Choice A
Only I and II
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
Choice A
2500
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
Choice C
–14.68%
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. a * \\frac{(b - d)}{c + b - d}\\)
2. a * \\frac{(b - d)}{c + b - 2d}\\)
3. a * \\frac{(c - b)}{b - d}\\)
4. a * \\frac{(b - d)}{c - d}\\)
Choice D
a * \\frac{(b - d)}{c - d}\\)
CAT Arithmetic: SICI - Moneylender

A moneylender takes advantage of difficult situation of poor people and charges 50% interest. However he never gets caught because he gives 20% of his total capital (initial capital + profit) as bribe. If in the beginning of 4th year, he has a capital of Rs 25,000 to invest, how much bribe did he give at the end of the second year?
1. Rs 4,900
2. Rs 5,200
3. Rs 5,000
4. Rs 6,000
Choice B
Rs 5,200
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
Choice B
600
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%
Choice D
-1%
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)
Choice A
600(A), 1200(B)
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
Choice B
23,367
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
Choice C
Rs.23,166.67
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%
4. More information required
Choice B
34.28%
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%
Choice B
30.3%
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 1^st and 3^rd worker combined.
1. 65%
2. 60%
3. 70%
4. 75%
Choice B
60%
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
Choice A
90 burgers

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

CAT 2023 Slot 3 - QA

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
1. 74000
2. 75000
3. 72000
4. 73000
Choice D
73000
CAT 2023 Slot 3 - QA

A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
1. 4.2%
2. 15.5%
3. 16%
4. 9.7%
Choice B
15.5%
CAT 2023 Slot 3 - QA

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
340
CAT 2023 Slot 2 - QA

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
1. 35.42%
2. 31.25%
3. 52%
4. 26%
Choice B
31.25%
CAT 2023 Slot 2 - QA

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
1. 45311
2. 51311
3. 33130
4. 40991
Choice B
51311
CAT 2023 Slot 2 - QA

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
407
CAT 2023 Slot 1 - QA

Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to
1. 42%
2. 47%
3. 45%
4. 49%
Choice B
47%
CAT 2023 Slot 1 - QA

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is
20808
CAT 2022 Slot 3 - QA

Nitu has an initial capital of \(₹ 20,000\). Out of this, she invests \(₹ 8,000\) at \(5.5 \%\) in bank \(A, ₹ 5,000\) at \(5.6 \%\) in bank \(B\) and the remaining amount at \(x \%\) in bank \(\mathrm{C}\), each rate being simple interest per annum. Her combined annual interest income from these investments is equal to \(5 \%\) of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been
1. 900
2. 700
3. 1000
4. 800
Choice D
800
CAT 2022 Slot 2 - QA

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
1. 40192
2. 60288
3. 50240
4. 62800
Choice D
62800
CAT 2022 Slot 2 - QA

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
20
CAT 2022 Slot 1 - QA

Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
160
CAT 2022 Slot 1 - QA

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
1. 62.5%
2. 37.5%
3. 60%
4. 40%
Choice B
37.5%
CAT 2021 Slot 3 - QA

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
1. 68.75
2. 68.50
3. 68.25
4. 69.25
Choice A
68.75

Correct: 17.6%
Incorrect: 11.34%
Unattempted: 71.06%
CAT 2021 Slot 3 - QA

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
1. 86
2. 84
3. 78
4. 80
Choice B
84

Correct: 56.39%
Incorrect: 11.19%
Unattempted: 32.42%
CAT 2021 Slot 3 - QA

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
1. 150
2. 225
3. 175
4. 200
Choice D
200

Correct: 22.96%
Incorrect: 17.67%
Unattempted: 59.37%
CAT 2021 Slot 3 - QA

Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is
1. 2436
2. 3436
3. 2346
4. 1436
Choice A
2436

Correct: 16.08%
Incorrect: 5.29%
Unattempted: 78.63%
CAT 2021 Slot 2 - QA

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is
250

Correct: 45.19%
Incorrect: 28.88%
Unattempted: 25.93%
CAT 2021 Slot 2 - QA

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu's share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is
1. 2400
2. 2200
3. 2000
4. 1800
Choice C
2000

Correct: 18.37%
Incorrect: 9.89%
Unattempted: 71.74%
CAT 2021 Slot 2 - QA

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
1. 15
2. 5
3. 10
4. 70
Choice C
10

Correct: 32.72%
Incorrect: 12.69%
Unattempted: 54.59%
CAT 2021 Slot 1 - QA

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
1. 127
2. 135
3. 124
4. 144
Choice A
127

Correct: 21.21%
Incorrect: 12.86%
Unattempted: 65.93%
CAT 2021 Slot 1 - QA

Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is
1000

Correct: 22.47%
Incorrect: 34.61%
Unattempted: 42.92%
CAT 2021 Slot 1 - QA

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to
1. 931.72
2. 926.84
3. 929.48
4. 934.65
Choice A
931.72

Correct: 36.05%
Incorrect: 16.86%
Unattempted: 47.09%
CAT 2020 Question Paper Slot 3 - Percentages

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
1. 399
2. 439
3. 357
4. 417
CAT 2020 Question Paper Slot 3 - Profit & Loss

A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
1. 35
2. 31
3. 22
4. 25
CAT 2020 Question Paper Slot 3 - Simple interest & Compound interest

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Correct Answer: 16000
CAT 2020 Question Paper Slot 2 - Simple interest & Compound interest

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Correct Answer: 90000
CAT 2020 Question Paper Slot 2 - Profit & Loss

Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
1. 60
2. 50
3. 55
4. 54
CAT 2020 Question Paper Slot 2 - Percentages

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?
1. 590
2. 580
3. 560
4. 570
CAT 2020 Question Paper Slot 1 - Simple interest & Compound interest

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Correct Answer: 12
CAT 2020 Question Paper Slot 1 - Profit & Loss

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

Correct Answer: 20000
CAT 2020 Question Paper Slot 1 - Percentages

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
1. 59
2. 62
3. 66
4. 55
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
Choice A
6600
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]
80
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
Choice D
4000
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]
20920
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
Choice A
1
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]
20
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
Choice D
70
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]
9
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
Choice A
80
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
Choice C
31
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 Ankit’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)
Rs. 4000
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 ﬁrst 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]
1,21,000
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
Choice B
243 ≤ N ≤ 252
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
Choice B
13000
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
Choice B
2000
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
Choice A
50
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
Choice C
10
CAT 2017 Question Paper Slot 1 - Percentages

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? (TITA)
20
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)
70000
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
Choice D
Sell at retail price
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
Choice D
65
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%
Choice B
8%
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%
Choice D
28%

The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.

XAT 2020 Question Paper - QADI
X, Y and Z start a web-based venture together. X invests Rs. 2.5 lakhs, Y invests Rs. 3.5 lakhs, and Z invests Rs. 4 lakhs. In the first year, the venture makes a profit of Rs. 2 lakhs. A part of the profit is shared between Y and Z in the ratio of 2:3, and the remaining profit is divided among X, Y and Z in the ratio of their initial investments.
The amount that Z receives is four times the amount that X receives. How much amount does Y receive?
1. Rs. 80,200
2. Rs. 75,000
3. Rs. 93,750
4. Rs. 74,250
5. Rs. 102,500
Choice B
Rs. 75,000
XAT 2019 Question Paper - QADI
A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:
A : p% and (p+1)%,
B : (p+2)% and (p-1)%,
C : (p+3)% and (p-2)%,
D : (p+4)% and (p-3)%,
E : (p+5)% and (p-4)%.

If all of them have the same salary at the end of two years, who got the least hike in his salary?
1. E
2. D
3. C
4. A
5. B
Choice A
E
XAT 2019 Question Paper - QADI
A ﬁrm pays its ﬁve clerks Rs. 15,000 each, three assistants Rs. 40,000 each and its accountant Rs. 66,000. Then the mean salary in the ﬁrm comprising of these nine employees exceeds its median salary by rupees
1. 14000
2. 14600
3. 15200
4. 15480
5. 14720
Choice A
14000
XAT 2019 Question Paper - QADI
An article is marked x% above the cost price. A discount of 2/3 x% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is?
1. 12
2. 16
3. 13
4. 15
5. 20
Choice D
15
XAT 2019 Question Paper - QADI
A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly installments. If the rate of interest charged is 12% per annum, then the amount of each installment (nearest to a rupee) is:
1. Rs.2880
2. Rs.2965
3. Rs.2896
4. Rs.2990
5. Rs.3016
Choice B
Rs.2965
XAT 2018 Question Paper - QADI
The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raised price. The discounted price again becomes P. If Y is the difference between X and Y, then find X.
1. 20
2. 25
3. 50
4. 100
5. None of the above
Choice D
100

The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

IPMAT 2020 Sample Paper - IPM Rohtak Quants

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
Choice B
4 Months
IPMAT 2020 Sample Paper - IPM Rohtak Quants

If x% of y is equal to z then what percentage of z is x?
1. \\frac{y^2}{100}\\)
2. \\frac{x^2}{100}\\)
3. \\frac{100^2}{y}\\)
4. \\frac{100^2}{x}\\)
Choice D
\\frac{100^2}{x}\\)
IPMAT 2020 Sample Paper - IPM Rohtak Quants

One Trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling prices are same, then the difference of their actual profit is Rs 85 and both claim to have made 20% profit. What is the selling price for each?
1. Rs 3000
2. Rs 2550
3. Rs 2800
4. Rs 4000
Choice B
Rs 2550
IPMAT 2020 Sample Paper - IPM Rohtak Quants

Due to increase of 20% in the price of eggs, 2 eggs less are available for Rs 24.The present rate of
eggs per dozen is
1. Rs 28.8/dozen
2. Rs 24.8/dozen
3. Rs 25.8/dozen
4. Rs 30/dozen
Choice A
RS 28.8/dozen
IPMAT 2020 Sample Paper - IPM Rohtak Quants

Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of the year, both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj?
1. 4 Months
2. 7 Months
3. 8 Months
4. 12 Months
Choice A
4 Months
IPMAT 2020 Question Paper - IPM Rohtak Quants

Present sum of money amounts to Rs 800 in two years and to Rs 920 in three years, then the present sum of money is
1. 420
2. 690
3. 560
4. None of the options
Choice C
560
IPMAT 2020 Question Paper - IPM Rohtak Quants

Bhavani invested an amount of Rs. 13900 divided in two different schemes, A and B at the simple interest rate of 14% per annum and 11% per annum respectively if the total amount of simple interest earned in two year be Rs. 3508, what was the amount invested in Scheme B?
1. 6400
2. 6500
3. 7200
4. 7900
Choice A
6400
IPMAT 2020 Question Paper - IPM Indore Quants

Ashok started a business with a certain investment. After few months, Bharat joined him investing half amount of Ashok's initial investment. At the end of the first year, the total profit was divided between them in ratio 3:1 . Bharat joined Ashok after
1. 2 months
2. 3 months
3. 4 months
4. 6 months
Choice C
4 months
IPMAT 2019 Question Paper - IPM Indore Quants

A shopkeeper reduces the price of a pen by 25% as a result of which the sales quantity increased by 20%. If the revenue made by the shopkeeper decreases by x% then x is

10
IPMAT 2019 Question Paper - IPM Indore Quants

If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent
1. 200%
2. 2%
3. 4%
4. 400%
Choice A
200%
IPMAT 2019 Question Paper - IPM Indore Quants

In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then
1. 20 ≤ x ≤ 50
2. x ≤ 20
3. x ≥ 50
4. 10 ≤ x ≤ 70
Choice A
20 ≤ x ≤ 50