# CAT Questions | CAT Arithmetic

###### CAT Quantitative Aptitude | CAT Ratios and Proportion, Mixtures, Alligations and Averages;

CAT Questions from Ratios and Proportions, Mixtures, Alligations and Averages are a part of CAT Arithmetic in the CAT Exam. They are regularly tested and have been constantly appearing in Quantitative Aptitude Section of CAT Exam. The concepts from Ratios and Proportions, Mixtures and Averages are particularly interesting as they are relatable and can be applied in real life scenarios. CAT exam does not only check for formulaic knowledge in this idea, but also for strong fundamentals and application of the concepts involved. One can usually expect 5~6 questions from these ideas in the CAT exam. 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 Averages : Maximum value

Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?

1. 40.18 kgs
2. 40.56 kgs
3. 40.67 kgs
4. 40.49 kgs

2. #### CAT Averages : Maximum possible value

The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is......

1. 99
2. 100
3. 87
4. 95

3. #### CAT Ratios and Proportions - Number Systems

The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

1. 99
2. 198
3. 330
4. 132

4. #### CAT Mixtures and Alligation - Fun question

Three friends A, B and C play a game in a pub. The rules are simple. Whenever there is a contest between any two of them, the one who has a higher percentage alcohol should pour 200 ml of his wine into the one having lower percentage alcohol. The game starts as a contest between A and B, then B and C and then C and A. Post this, the game continues in the same cycle on and on. If a player has emptied all his alcohol, then the remaining two play the game with the same rules. If two players have the alcohol of the same percentage level, the younger one pours 200 ml of his alcohol into the elder one’s glass. All three of them start the game with 600 ml of wine. A’s wine has 60% alcohol, B’s has 48% alcohol and C’s has 50% alcohol. They take 3 minutes to play one round of this game. D, a fourth friend leaves the pub immediately after the game begins, returns after an hour and drinks wine from the person who has the highest alcohol percentage. What is the concentration of the alcohol that D had?

1. 51.5%
2. 52.67%
3. 53%
4. Cannot be determined

5. #### CAT Averages - Range

5 Scores in a classroom are broken into 5 different ranges, 51-60, 61-70, 71-80, 81-90 and 91-100. The number of students who have scored in each range is given below.
51 to 60 - 3 students, 61 to 70 - 8 students, 71 to 80 - 7 students, 81 to 90 - 4 students, 91 to 100 - 3 students.
Furthermore, we know that the number of students who scored 76 or more is atleast one more than those who scored below 75. What is the minimum possible average overall of this class?

1. 72
2. 71.2
3. 70.6
4. 69.2

6. #### CAT Averages - Mean Median

The median of n distinct numbers is greater than the average, does this mean that there are more terms above the average than below it?

7. #### CAT Averages - Mean and Range

In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?

1. 2.8 kgs
2. 3.2 kgs
3. 3 kgs
4. 4 kgs

8. #### CAT Ratios - Linear Equations

Janta Airline has a free luggage allowance for its passengers. If any passenger carries excess luggage, it is charged at a constant rate per kg. The total luggage charge paid by Ravind Jekriwal and Pranas Shubhan is Rs. 1100. If both Ravind and Pranas had carried luggage twice the weight than they actually did, their luggage charges would have been Rs. 2000 and Rs. 1000 respectively. What was the charge levied on Ravind’s luggage?

1. Rs. 800
2. Rs. 700
3. Rs. 600
4. Rs. 900

9. #### CAT Mixtures and Alligations - Number Systems

1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

1. 19
2. 20
3. 21
4. 13

10. #### CAT Averages - Mean Median

In a sequence of 25 terms, can 20 terms be below the average? Can 20 terms be between median and average?

11. #### CAT Averages - Sets of numbers

From 10 numbers, a, b, c,...j, all sets of 4 numbers are chosen and their averages computed. Will the average of these averages be equal to the average of the 10 numbers?

12. #### CAT Mixture of two mixtures

Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the ratio 5 : 3. If the number of students in Class A is at least twice as many as the number of students in Class B, what is the minimum percentage of boys when both classes are considered together?

1. 33.33%
2. 40%
3. 39.17%
4. 37.5%

13. #### CAT Averages - Mixtures

School X has 3 classes, A, B and C. The average score of Class B is 16 more than the average score of class C. The strengths of Classes A, B and C are in the ratio 2:3:5, respectively. If the average score of the school 2 less than the average score of Class A, Find the difference between average of class A and class C.

14. #### CAT Averages - Sets of numbers

Natural numbers 1 to 25 (both inclusive) are split into 5 groups of 5 numbers each. The medians of these 5 groups are A, B, C, D and E. If the average of these medians is m, what are the smallest and the largest values m can take?

15. #### CAT Mean and Range

Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?

16. #### CAT Mixtures - Alloys

100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

1. 100 kgs ≤ x ≤ 200 kgs
2. 80 kgs ≤ x ≤ 240 kgs
3. 110 kgs ≤ x ≤ 220 kgs
4. 75 kgs ≤ x ≤ 250 kgs

17. #### CAT Mean, median, maximum

The average of 5 distinct positive integers if 33. What are the maximum and minimum possible values of the median of the 5 numbers if the average of the three largest numbers within this set is 39?

18. #### CAT Change in average

Consider 5 distinct positive numbers a, b, c, d, and e. The average of these numbers is k. If we remove b from this set, the average drops to m (m is less than k). Average of c, b, d and e is K. We also know that c is less than d and e is less than k. The difference between c and b is equal to the difference between e and d. Average of a, b, c and e is greater than m. Write down a, d, c, d and e in ascending order.

19. #### CAT Mean, Median, Maximum, Minimum

Average of 6 distinct positive integers is 33. The median of the three largest numbers is 43. What is the difference between the highest and lowest possible median of the 6 numbers?

20. #### CAT Ratios of two mixtures

In class A, the ratio of boys to girls is 2 : 3. In class B the ratio of boys to girls is 4 : 5. If the ratio of boys to girls in both classes put together is 3 : 4, what is the ratio of number of girls in class A to number of girls in class B?

21. #### CAT - Number of students

A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got! How many students were there in the class?

1. 30
2. 26
3. 11
4. 31

22. #### CAT - Age of the twin children

The average age of a couple was 24 years. After their 1st and 2nd children (twins) were born, the average age of the family became 13.5 years. The average age of the family just after 3rd child was born was 13.2 years. The average age of the family after 4th child was born was 16 years. The current average age of the family is 19 years. What is the current age of the twin children?

1. 14 years
2. 15 years
3. 11 years
4. 12 years

23. #### CAT - Minimum number of fruits

A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?

1. 240
2. 360
3. 120
4. 90

24. #### CAT - Number of coins

A, B and C have a few coins with them. 7 times the number of coins that A has is equal to 5 times the number of coins B has while 6 times the number of coins B has is equal to 11 times the number of coins C has. What is the minimum number of coins with A, B and C put together?

1. 110
2. 174
3. 154
4. 165

25. #### CAT Mixtures and Alligation

6 kg of Rs 8/kg wheat is mixed with 3 kg of another type of wheat to get a mixture costing Rs 10/kg. Find the price of the costlier wheat.

1. Rs 12/kg
2. Rs 14/kg
3. Rs 16/kg
4. Rs 6/kg

26. #### CAT Mixtures and Alligation

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

1. $$frac{2187}{100}\\$ 2. $\frac{81}{19}\\$ 3. $\frac{729}{271}\\$ 4. $\frac{743}{229}\\$ 27. #### CAT Mixtures and Alligation 40% of a club’s revenue comes from people of 25 years of age while 60% of its revenue comes from people of 35 years of age. If the club raises its fee by 20% for its 25 years old members and 30% for 35 years old members, what is the percentage increase in overall revenue of the club? 1. 26% 2. 25% 3. 24% 4. 23% 28. #### CAT Mixtures and Alligation A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture? 1. 3.33 litres 2. 4 litres 3. 5.67 litres 4. 7.14 litres 29. #### CAT Mixtures and Alligation Ram borrows Rs 4000 on simple interest from Shyam for a period of 4 years. He borrows a portion of amount at 2% interest and the remaining at 5%. If the interest Shyam earns is Rs 480, How much money did Ram borrow at 2% interest rate? 1. $\frac{8000}{3}\\$ 2. $\frac{4000}{3}\\$ 3. 3000 4. 2000 30. #### CAT Mixtures and Alligation A milkman purchases milk at Rs 20/litre and mixes 4 litres of water in it. By selling the resultant mixture at the rate of Rs 20/litre, he earns a profit of 40%. The amount of mixture he had with him to sell was: 1. 10 litres 2. 12 litres 3. 14 litres 4. 4 litres 31. #### CAT Averages : Alligation What is the ratio in which water should be mixed with a coke concentrate costing Rs 15/litre to make a profit of 30% by selling the resultant drink at Rs 18/litre? 1. 12:1 2. 11:1 3. 1:10 4. 1:12 32. #### CAT Averages : Alligation A mixture of 40 litres of milk and water, contains 20% of water. How much water must be added to the above mixture to make the water 25% of the resultant mixture? 1. 3 l 2. 2.33 l 3. 2.67 l 4. 4 l 33. #### CAT Ratios - Alligation A man buys juice at Rs 10/litre and dilutes it with water. He sells the mixtures at the cost price and thus gains 11.11%. Find the quantity of water mixed by him in every litre of juice. 1. 0.1 l 2. 0.909 l 3. 0.125 l 4. 0.111 l 34. #### CAT Mixtures - Alligation Two tanks of similar volume are full of a mixture of oil and water. In the first, the ratio of oil and water is 5:8 and in the second, it is 7:19. If both these tanks are poured in a larger tank, what would be the resultant ratio of oil and water? 1. 1:3 2. 17:52 3. 151:304 4. 17:35 35. #### CAT Averages - Alligation A vessel is full of a mixture of methanol and ethanol in which there is 20% ethanol. 10 litres of mixture are drawn off and filled with methanol. If the ethanol is now 15%, what is the capacity of the vessel? 1. 40 l 2. 30 l 3. 50 l 4. 36 l 36. #### CAT Alligation In Kaziranga national park, the residents are either Hippopotamus or Peacocks. When the heads are counted, it comes out to be 96 and when the legs are counted it is 336 in number. Find the number of peacocks in the park. 1. 72 2. 24 3. 48 4. 80 37. #### CAT Alligation What would be the ratio of milk and water in a final mixture formed by mixing milk and water that are present in three vessels of capacity 1l, 2l, and 3l respectively and in the ratios 5:1, 3:2 and 4:3 respectively? 1. 747:443 2. 787:1260 3. 787:473 4. 747:473 38. #### CAT Averages A group of 20 people has the oldest person with 90 years of age. The average of the group is reduced by 4, if the oldest person is reduced by someone new, Find the age of the new person. 1. 80 years 2. 60 years 3. 30 years 4. 10 years 39. #### CAT Averages Ram travels half of his journey by train at 80 kmph, half of the remaining with bus at 40 kmph and the rest with cycle at 20 kmph. Find his average speed during the entire journey. 1. 33.33 kmph 2. 40 kmph 3. 50 kmph 4. 45 kmph 40. #### CAT Averages Sambhunath had a great job in India but he went abroad to earn more money. He realized he had to make at least USD 6000/month in order to justify his foreign trip. He recorded an average of USD 5,500/ month for the first 11 months. What should be his earning on the last month in order for his foreign visit to make sense? 1. 9500 2. 11,500 3. 11,000 4. 10,500 41. #### CAT Averages : A group of people decided to cut 128 trees in a certain number of days. For the first 4 days, they were able to achieve their planned per day target. However, for the remaining days, the group was able to cut 4 more trees daily than planned. In this way, the group had cut 164 trees one day before the planned finish date. What was the number of trees the group was planning to cut per day? 1. 16 2. 32 3. 8 4. 64 42. #### CAT Averages : There are 500 rooms in a multi-floored hotel. However, due to a change in rule, the hotel has to decrease the number of floors by 5. However, the management is able to put 5 more rooms in each floor. Over all, the number of rooms in the hotel decreases by 10%. Find the number of floors and the number of rooms/floor the hotel originally had? 1. 10 floors 50 rooms 2. 20 floors 20 rooms 3. 20 floors 25 rooms 4. 50 floors 10 rooms 43. #### CAT Averages For a global sports event, Nike has to make 810 pair of shoes while Adidas has to make 900 pair of shoes, in the same period of time. Nike could complete the order 3 days before the scheduled time while Adidas completed the order 3 days before Nike. How many pair of shoes did each make per day if Adidas made 21 more shoes per day than Nike? 1. 44 and 65 2. 21 and 42 3. 34 and 55 4. 54 and 75 44. #### CAT Averages In olympics, a game has 2 groups A and B having participants from 20 and 25 countries respectively having an average score of 20 and 25 respectively. Also, A: Highest score: 25 Lowest score: 15 B: Highest score: 32 Lowest score: 24 What can be the minimum and maximum value of B’s average if 5 teams are transferred from A to B? 1. 25 and 25 2. 22.5 and 25 3. 23.33 and 26 4. 23.33 and 25 45. #### CAT Averages In the previous question, what can be the minimum and maximum value of A’s average if 5 teams are transferred from B to A? 1. 20.8 and 22.4 2. 20.6 and 22.6 3. 20.8 and 22.8 4. 20.8 and 21.8 46. #### CAT Averages If the average of 9 consecutive number is T. How much will the average increase by if the next 3 consecutive numbers are also added? 1. 3 2. 1.5 3. T 4. Can’t be determined 47. #### CAT Averages If the product of n distinct positive integers is nn. What is the minimum value of their average if n = 6? 1. 6 2. 10 3. $\frac{46}{6}\\$ 4. 8 48. #### CAT Averages If M is a positive integer such that average of 31, 33, M, 36. 37 lies b/w 40 and 43$both inclusive). What is the number of possible values of M?

1. 16
2. 20
3. 24
4. No such M exists

49. #### CAT Averages

Average of ‘n’ number is t. One of the numbers ‘s’ is replaced by ‘z’ and the new average becomes u. What is the relation b/w n, t, s, u and z?

1. $$frac{$u-3$}{(z-s)}$ = $\frac{1}{n}\\$ 2. $\frac{$z-s$}{u}$ = $\frac{1}{n}\\$ 3. $\frac{$t-u$}{(s-z)}$ = $\frac{1}{n}\\$ 4. $\frac{$u-3$}{(z-s)}$ = $\frac{1}{n}\\$ 50. #### CAT Averages Arun has 13 boxes of chocolates with him, with an average of 17 chocolates per box. If each box has at least 11 chocolates and no two boxes have equal number of chocolates, then what can be the maximum possible number of chocolates in any box? 1. 23 2. 25 3. 29 4. Can't be determined 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. 1. #### CAT 2021 Slot 3 - QA If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is 1. 3 2. 2.5 3. 4 4. 3.5 2. #### CAT 2021 Slot 3 - QA The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is 1. #### CAT 2021 Slot 3 - QA One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be 1. 20800 2. 20200 3. 20500 4. 20000 2. #### CAT 2021 Slot 3 - QA A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is 1. #### CAT 2021 Slot 2 - QA From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is 1. #### CAT 2021 Slot 2 - QA In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is 1. #### CAT 2021 Slot 2 - QA A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is 1. 692 2. 688 3. 653 4. 675 2. #### CAT 2021 Slot 1 - QA A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is 1. 12 2. 13 3. 11 4. 10 3. #### CAT 2021 Slot 1 - QA Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to 1. 18 2. 26 3. 16 4. 20 4. #### CAT 2021 Slot 1 - QA The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is 1. #### CAT 2021 Slot 1 - QA Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was 1. #### CAT 2021 Slot 1 - QA The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is 1. 7 : 3 2. 11 : 3 3. 11 : 7 4. 3 : 2 2. #### CAT 2020 Question Paper Slot 3 - Averages Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is 3. #### CAT 2020 Question Paper Slot 3 - Averages A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is 1. 1 2. 3 3. 2 4. 4 4. #### CAT 2020 Question Paper Slot 3 - Mixtures Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is 1. 94% 2. 92% 3. 90% 4. 89% 5. #### CAT 2020 Question Paper Slot 2 - Averages In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by 1. 5 2. 3 3. 4 4. 6 6. #### CAT 2020 Question Paper Slot 2 - Ratio & Proportions A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is 7. #### CAT 2020 Question Paper Slot 1 - Averages Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is 1. 6 2. 4 3. 7 4. 5 8. #### CAT 2020 Question Paper Slot 1 - Mixtures An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is 1. 84 2. 48 3. 96 4. 70 9. #### CAT 2020 Question Paper Slot 1 - Ratio & Proportions A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3? 10. #### CAT 2019 Question Paper Slot 2 - Averages The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers? 1. 4 2. 5 3. 4.5 4. 3.5 11. #### CAT 2019 Question Paper Slot 2 - Ratio & proportion In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:3. Then Anjali's score exceeded Rama's score by 1. 26 2. 32 3. 24 4. 35 12. #### CAT 2019 Question Paper Slot 2 - Ratios and proportions 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 1. 7 2. 8 3. 9 4. 10 13. #### CAT 2019 Question Paper Slot 2 - Mixtures The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is 1. 15 2. 12 3. 13 4. 14 14. #### CAT 2019 Question Paper Slot 1 - Ratios and proportions Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income$in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?

1. 7000
2. 6000
3. 6350
4. 7250

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

A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is

1. 70
2. 85
3. 80
4. 75
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16. #### CAT 2019 Question Paper Slot 1 - Averages

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

1. 51
2. 53
3. 49
4. 48

17. #### CAT 2018 Question Paper Slot 2 - Ratio & Proportion | Mixtures & Alligations

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio

1. 251 : 163
2. 239 : 161
3. 220 : 149
4. 229 : 141

18. #### CAT 2018 Question Paper Slot 2 - Mixtures

A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is

1. 50%
2. 55%
3. 48%
4. 52%

19. #### CAT 2018 Question Paper Slot 2 - Mixtures and Alligations

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now

1. 25.4
2. 20.5
3. 30.3
4. 35.2

20. #### CAT 2018 Question Paper Slot 2 - Ratio & Proportions

The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. The ratio of Bimal’s new score to that of his original score is

1. 3 : 2
2. 4 : 3
3. 5 : 4
4. 8 : 5

21. #### CAT 2018 Question Paper Slot 2 - Ratio & Proportions | Mixtures & Alligations

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is

1. 3 : 10
2. 1 : 3
3. 2 : 5
4. 1 : 4

22. #### CAT 2018 Question Paper Slot 1 - Mixtures and Alligations

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

1. 20
2. 16
3. 22
4. 26

23. #### CAT 2018 Question Paper Slot 1 - Averages

A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is [TITA]

1. #### CAT 2018 Question Paper Slot 1 - Ratio & Proportions

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

1. 21 : 25
2. 19 : 24
3. 18 : 25
4. 17 : 25

2. #### CAT 2018 Question Paper Slot 1 - Mixtures

A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

1. 84
2. 86
3. 96
4. 98

3. #### CAT 2018 Question Paper Slot 1 - Ratio and Proportion

Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju?

1. $$frac{1}{4}$ 2. $\frac{1}{5}$ 3. $\frac{6}{19}$ 4. $\frac{7}{33}$ 4. #### CAT 2018 Question Paper Slot 1 - Averages In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years? 1. 25 2. 26 3. 27 4. 28 5. #### CAT 2017 Question Paper Slot 2 - Mixtures Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio? 1. 27 : 14 2. 27 : 13 3. 27 : 16 4. 27 : 18 6. #### CAT 2017 Question Paper Slot 2 - Averages The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is 1. 30 2. 28 3. 32 4. 26 7. #### CAT 2017 Question Paper Slot 2 - Ratios If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of$a + b + c)?

1. 201
2. 205
3. 207
4. 210

8. #### CAT 2017 Question Paper Slot 2 - Mixtures

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

1. The same amount of water and liquid B
2. The same amount of liquids B and C
3. More water than liquid B
4. More water than liquid A

9. #### CAT 2017 Question Paper Slot 1 - Averages

An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group? (TITA)

1. #### CAT 2017 Question Paper Slot 1 - Ratio & Proportions

Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:

1. 438 crore
2. 435 crore
3. 348 crore
4. 345 crore

2. #### CAT 2017 Question Paper Slot 1 - Ratio & Proportions

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio:

1. 1 : 1
2. 8 : 7
3. 4 : 3
4. 6 : 5

3. #### CAT 2017 Question Paper Slot 1 - Mixture & Alligation

A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is:

1. 9.5
2. 10
3. 4.5
4. 6

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.

1. #### XAT 2018 Question Paper - QADI

A mixture comprises water and liquids A and B. The volume of water is 1/3 of the total mixture and the volume of liquids A and B are in the ratio 5:3. To remove the water, the mixture is passed through a porous medium which completely absorbs the water and partially absorbs liquid A. Altogether this porous medium absorbs 200 ml of the initial mixture. If the ratio of volume of liquids A and B in the residual concentrated mixture becomes 7:9 then find the volume of water absorbed by the porous medium.

1. 60 ml
2. 200/3 ml
3. 80 ml
4. 100 ml
5. 120 ml

2. #### XAT 2018 Question Paper - QADI

This question is followed by two statements. These statements provide data that mayhelp answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions.

Accordingly, choose the appropriate option given below the questions.
A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?
Statement I: All members are between 50 and 85 years of age.
Statement II: The standard deviation of their ages is 4.6.

1. Statement I alone is sufficient to answer.
2. Statement II alone is sufficient to answer.
3. Either of the statement is sufficient to answer.
4. Both statements are required to answer.

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.

1. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants

A Container contains X Litres of Milk. A thief stole 50 Litres of Milk and replaced it with the same quantity of water. He repeated the same process further two times. And thus Milk in the container is only X-122 litres. Then what is the quantity of water in the final mixture?

1. 122 Litre
2. 124 Litre
3. 128 Litre
4. 250 Litre

2. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants

Given ratio are a : b = 2 : 3, b : c = 5 : 2, c : d = 1 : 4. Find a : b : c.

1. 2 : 3 : 6
2. 4 : 5 : 6
3. 10 : 15 : 6
4. 1 : 5 : 7

3. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants

If there are Rs 495 in a bag in denominations of one-rupee, 50 paisa and 25 paisa coins, which are in the ratio 1 : 8 : 16. How many 50 paisa coins are there in the bag?

1. 50
2. 220
3. 440
4. None of these

One-fifth of a number is equal to $$frac{5}{8}\\$th of another number. If 35 is added to the first number, it becomes four times of the second number. Find the second number. 1. 39 2. 70 3. 40 4. 25 5. #### IPMAT 2020 Question Paper - IPM Rohtak Quants The average age of a group of 9 friends is 22 years. LAVGIR is the youngest and his age is 6 years, then what happened to be the average age of the family just before LAVGIR was born? 1. 18 2. 7 3. 20 4. 24 6. #### IPMAT 2020 Question Paper - IPM Rohtak Quants Average stipend of summer internship of an institute is Rs. 20000 per month. Recently the institute announced increment of Rs. 2000 per month for all the students. The new average stipend of students will now be? 1. 22000 2. 23000 3. 24000 4. 25000 7. #### IPMAT 2020 Question Paper - IPM Rohtak Quants The average presence of employees of a company for yoga sessions in an office on Monday, Tuesday and Wednesday is thirty two and on the Wednesday, Thursday, Friday and Saturday is thirty. If the average number of employees on all the six days is twenty six then the number of employees who attended the sessions on Wednesday is? 1. 38 2. 40 3. 60 4. 64 8. #### IPMAT 2020 Question Paper - IPM Rohtak Quants The average spending of Lata Mangeshkar for the part of week from Monday to Saturday is Rs. 4200. She spent Rs. 1200 on Monday and Rs. 1500 on Sunday that week. The average spending for the part of week from Tuesday to Sunday that week is? 1. 4100 2. 4200 3. 4250 4. 4300 9. #### IPMAT 2020 Question Paper - IPM Indore Quants Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio 4: 1 and paid Rs. I 12 . The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________. 10. #### IPMAT 2020 Question Paper - IPM Indore Quants Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water? 1. 1 2. 2 3. 3 4. 4 11. #### IPMAT 2020 Question Paper - IPM Indore Quants The average marks of 6 students in a test is 64 . All the students got different marks, one of the students ohtained 70 marks and all other students scored 40 or above. The maximum possible difference between the second highest and the second lowest marks is 1. 50 2. 54 3. 57 4. 58 12. #### IPMAT 2019 Question Paper - IPM Indore Quants Three friends divided some apples in the ratio 3 : 5 : 7 among themselves. After consuming 16 apples they found that the remaining number of apples with them was equal to largest number of apples received by one of them at the beginning. Total number of apples these friends initially had was 13. #### IPMAT 2019 Question Paper - IPM Indore Quants The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is 14. #### IPMAT 2019 Question Paper - IPM Indore Quants An alloy P has copper and zinc in the proportion of 5: 2$by weight), while another alloy Q has the same metals in the proportion of 3: 4 (by weight). If these two alloys are mixed in the proportion of a : b (by weight), a new alloy R is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy S, formed by mixing the two alloys P and Q in the proportion of b : a (by weight) is

1. 7 : 9
2. 9 : 7
3. 9 : 5
4. 5 : 9

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