Average is a foundational and frequently tested topic in Arithmetic for CAT 2026, forming the base for several higher-order Quant problems. Practice curated CAT arithmetic important questions built around repeated average concepts, weighted averages, and data-based applications seen in recent CAT exams. These questions are designed to sharpen your calculation speed and conceptual accuracy for CAT 2026.
51. Anna, Ben and Clark have an average amount of Rs. 93. If Anna gives Rs. 12 to Ben, then average amount with Ben and Clark would be Rs. 108 whereas if Clark gives Rs. 25 to Anna, then average amount with Anna and Ben would be Rs. 98. What is the amount (in Rs.) with Ben?
52. The average of five natural numbers is 100. The largest number among these exceeds the smallest number by 60. The rest of the three numbers lie between these two numbers and are all equal. How many sets of the five numbers is possible?
53. From the first ‘n’ consecutive even natural numbers written on a blackboard, one of the numbers is removed. If the average of the remaining numbers remains is 32, then which of the following cannot be the value of ‘n’?
54. Seven students appeared for an exam in which the maximum marks were 100. The marks scored by the students in the exam were found to be seven distinct integer values. The arithmetic mean of their marks was 85 whereas the median of their marks was 90. What could be the maximum difference between the marks of any two students?
55. The mean and median of Ashok’s 7 scores is 74. If his lowest 2 scores are not considered, the mean increased by 1 whereas the median remained the same. What is the highest score he could have got, if all his scores were whole numbers and no number except 74 appears more than once?
56. The average marks of ‘m’ students in class-IV is ‘n’. When the marks of one student Yatin are also included, the average of the students increases to ‘n + 1’. If we further include the marks of another student Nitin, the average of the class increases to ‘n + 2’. What is the difference between the marks scored by Nitin and Yatin?
57. Jatin has 20 pencils of different lengths. If four longest pencils are removed, the average length of the pencils with him reduces by 1.75 cm. If the average length of these 4 longest pencils is 1.7 times that of the average length of the 20 pencils, then the average length of the remaining 16 pencils is:
58. A cricket player’s average score increases by 2 if the first 15 innings are not considered, and decreases by 2 if the last 15 innings are not considered. What is the number of innings the cricketer has played if his average scores for the first 15 and the last 15 innings are 17 and 25, respectively?
59. In a tweeter campaign run by a famous channel, on an average, there were 115 responses per second on Monday in 24 hours. The average number of tweets in the last 4 hours was 215 per second. What is the average number of tweets per hour in the first 20 hours?
60. The marks scored by 10 students in the first unit test are 75, M2, M3, …, M8, M9 and 93 when arranged in an ascending order. The average of M2, M3, …, M7 is 82 and the average of M4, M5, …, M9 is 86. Find the difference between the average of three lowest scores and the average of three highest scores.
61. The average quantity of sugar purchased by 16 customers is 8 kg. The maximum quantity purchased was 25 kg and the minimum quantity purchased was 5 kg. If ‘A’ is the average when the minimum quantity purchased is not considered and ‘B’ is the average when the maximum quantity purchased is not considered, what must be the difference between the A and B?
62. Jatin bought 225 pens on Monday. On Tuesday he bought 150 more pens at Rs. 6.05 per pen. Due to this the average price per pen turned out to be Rs. 22.25. Find the average price of pens bought on Monday.
63. Class V has two divisions A and B. The average weight of the students of division A is 22 kg while that of division B is 33 kg. One student from division B whose weight is same as the average weight of the students in his division is shifted to division A and two division A students with average weight 22 kg are shifted to division B. After the transfer, the sum of weights of all the students of division A is 209 which is less by 198 than that of division B. Find average weight of the students in the two divisions taken together (in kg).
64. The average marks scored by the students of a class increases by 1 if a new student who scored 81 joins the class. If one more student with 62 marks joins the class, the average of the class further increases by 0.5. How many students were originally there in the class?
65. Average of a set of 30 distinct positive integers is 155, which is also the median of the set. The median of the last 15 integers (when arranged in ascending order) in the set is 230. Which of the following can be the average of the first 15 integers, when they are arranged in the ascending order?
66. Mithilesh calculates his average marks in seven subjects in which maximum marks awarded were 99. By mistake he writes the digits of the scores of two subjects in the reverse order of original marks thereby increasing the average by 9 marks. If the incorrect numbers are in the ratio 8: 7, what is the total of the original scores in the two subjects?
67. Srinath earned Rs 1.6 lakh per month from January to June after which there was a steady increase of Rs.10,000 per month for four months. The average monthly income of Srinath for the whole year was Rs 1.8 lakh. If the income for December was 20% more than that of October, then what was his monthly income (in Rs.) for November?
68. Class A has 6 less students than class B. The sum of total marks obtained by class A students were 288 and that of class B were 396 in the same test. If the average marks obtained by class A students were 2 more than the average marks obtained by class B students, then the sum total number of students of class A and class B are:
69. From a class of 50 students with roll numbers 1, 2, 3, …, 50, some students were selected for an event but the condition was that their roll numbers should be either a multiple of 3 or a multiple of 4. The average weight of all the students who were not selected was 48 kg and the average weight of all the students who were selected was 44 kg. What was the average weight (in kg) of the class?
70. A shopkeeper has four packets of sugar which he wants to weigh. The aggregate weight of the packets of sugar taken two at a time is 19 kg, 26 kg, 29 kg, 31 kg, 34 kg and 41 kg. If a fifth packet of sugar has to be added such that the average weight now becomes 3 kg higher than the original average, then what is the average (in kg) of the new packet of sugar?
71. There are five friends A, B, C, D and E. The weights of A, B and C are 92%, 111% and 93% respectively of the average weight of all five. The ratio of the weights of D and E is 7: 10. The difference between the weights of D and E is 18 kg. What is the average weight (in kg) of B and C?
72. There are 2n integers [0, 0, 1, 1, 2, 2 ,…, (n – 1), (n – 1)]. From these 2n integers, n integers are chosen such that their average is an integer. Find the minimum average of those chosen n integers, given that n = 19.
73. A cricketer has played in 45 innings and his average score is 50. Out of these 45 innings he did not score more than 50 in exactly 30 innings. What is the highest possible value of the average score in these 30 innings?
74. Binoy, Badal and Dinesh are employees of a trading company where the salary of Dinesh is one-fifth of the sum of the salaries of Binoy and Badal. After an annual appraisal, the salary of Binoy and Badal increased by Rs. 5000 each and that of Dinesh increased by Rs. 7000. Find the average salary of the three before the increment if the revised salaries of Binoy, Badal and Dinesh are in the ratio 7: 8: 4.
75. A class test was conducted in all three sections of class X and all students wrote it. The average score in section A is 67, in section B is 62, and in section C is 57. The average score of all students in sections A and B together is 64. The average score of all students in sections B and C together is 60. What is the average score for all the three sections?
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