1EasyMCQ
Five years ago, the average age of A, B and C was 25 years and that of B and C ten years ago was 20 years. A’s present age is
- A
30 years
- B
35 years
- C
40 years
- D
48 years
Averages Questions for CAT
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250 easy154 medium99 hard
Averages look like the easiest topic in CAT arithmetic and produce more silent errors than almost any other, because averaging averages is wrong in most situations candidates apply it to. The reliable method is to work with totals rather than means: convert every average back into a sum, combine the sums, and divide once at the end. Weighted average and alligation questions are the same idea, and practising them together is what makes the connection stick.
20 free Averages questions
2EasyTITA
The average age of a family of 3 members is 30 years. If the age of the youngest member is 5 years, then what was the average age of the family immediately prior to the birth of the youngest member?
3EasyMCQ
The average of N natural numbers each of which less than 100 is 75. If a1 which is the smallest number is increased by 20, aN which is the largest number is decreased by 10, then the resultant average is 80. If (a1)new ≤ (a2)new, then the number of sets of these N natural numbers is:
- A
10
- B
24
- C
25
- D
51
4EasyMCQ
The average age of 60 students is 23 years. 40 faculty members have an average age of 35. Find the new average.
- A
27 years
- B
26.5 years
- C
27.8 years
- D
28 years
5EasyMCQ
The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is:
- A
11.5
- B
11.4
- C
11.3
- D
11.0
6EasyMCQ
The average of 9 numbers is 12. What is their total sum?
- A
100
- B
108
- C
112
- D
120
7MediumMCQ
Nine years ago, the ages of the members of a family of twelve added up to 468 years. Three years later, one member died at the age of 70 years and a child was born during the same year. Four years after that, one more member died, again at 70, and a child was born during the same year. The current average age of this twelve-member family is nearest to
- A
35 years
- B
36 years
- C
37 years
- D
38 years
8MediumMCQ
The average age of a group of 15 persons is 25 years and 5 months. Two persons, each 40 years old, left the group. What will be the average age of the remaining persons?
- A
23.17 years
- B
24.25 years
- C
25.35 years
- D
25 years
9MediumMCQ
Six students, including Ravi, appear for an exam with integer marks between 0 and 60. The average marks of all six students is 40, and exactly four of them scored more than 35. If no two students obtained the same marks and Ravi scored the least among them, then the difference between the highest and lowest possible marks of Ravi is
- A
18
- B
20
- C
22
- D
24
10MediumTITA
Ravi took the MAT exam consisting of 140 questions (4 marks for correct answers, -1 for wrong answers, and 0 for unattempted questions). He scored 240 marks. If the maximum number of correct answers is m and the minimum is n, calculate m-n.
11MediumTITA
If the average of 21, 23, x, 24, 27 lies in between 25, 28 (including both). Find the number of possible integral values of x.
12MediumMCQ
In India, there are two kinds of athletes, amateur athletes and elite athletes. Amateur athletes spend an average of Rs. 20,000 per year and constitute 70% of the total athletes. If the average expenditure of all the athletes is Rs. 29,000, what is the average expenditure of elite athletes?
- A
Rs. 38,000
- B
Rs. 49,000
- C
Rs. 50,000
- D
Rs. 42,000
13MediumMCQ
A student’s average score in 8 tests is 70. If the highest and lowest marks are removed, the average of the remaining 6 tests becomes 72. If the highest score was 88, what was the lowest score?
- A
40
- B
44
- C
56
- D
58
14MediumMCQ
A class of 40 students + 1 teacher has average weight of 48 kg. Teacher leaves, avg drops by 1.25%. 2 students join, avg drops by 0.4 kg more. Find average weight of the 2 new students.
- A
39
- B
40
- C
41
- D
42
15HardMCQ
The average of the first natural numbers is 15.5. Three consecutive numbers among these numbers are selected, each having the same digit in the tens place. If these three numbers are replaced by the numbers written in the reversed order of their digits, the average increases by 0.9. What is the maximum possible sum of the original three consecutive numbers?
- A
48
- B
69
- C
36
- D
90
16HardMCQ
Akhil's score is 50% lower than Ella's score. Dinesh's score is 25% higher than Akhil's. Bharat scored 10% less than Ella. Chandu's score is 30% higher than Dinesh's. Given that the median score is 390. If, in re-evaluation, the score of Akhil is increased by 25%, the score of Dinesh is reduced by 20%. Find the average score of all five students after re-evaluation.
- A
368.4
- B
366.4
- C
368.2
- D
366.2
17HardMCQ
A series of 7 experiments is being conducted to measure the density of a liquid. The density of the liquid is the average of the values obtained in the 7 experiments. This value is obtained as . The average obtained in the first three experiments is 18.5. The value obtained in the 4th experiment is 1 greater than that obtained in the 5th. The average of the 6th and 7th experiments is 2.5 more than the average of the first three. What is the density of the liquid obtained in the 4th experiment?
- A
18.5
- B
19.6
- C
20.4
- D
17.5
18HardMCQ
If the average of 5 distinct positive integers is 33, what are the maximum and minimum possible values for the median of these numbers, given that the average of the three largest numbers is 39?
- A
Min is 23, Max is 40
- B
Min is 25, Max is 39
- C
Min is 26, Max is 38
- D
Min is 24, Max is 37
19HardMCQ
A company has 50 employees listed in order. In 2022, the average bonus of the first 35 employees was Rs. 30000, of the last 35 employees was Rs. 70000, and of the first 15 and last 15 employees together was Rs. 60000. In 2023, the bonus of the first 15 employees doubled, of the last 15 employees tripled, and the rest remained unchanged. What was the average bonus of all 50 employees in 2023?
- A
88000
- B
121000
- C
95000
- D
100000
20HardTITA
In an exam, the average marks of two sections C and D are 28 and 52 respectively. The number of students in section C is 6 less than that in section D. If the average of all students combined is an integer, then the difference between the maximum and minimum possible number of students in section C is
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Averages for CAT, answered
What CAT asks in Averages, the mistakes that cost the most marks, and how to practise it.
Simple averages, weighted averages, the effect of adding or removing an element, average speed (which is not the average of the speeds), and alligation-style mixture questions where two groups with known averages are combined.
Because each average represents a different number of items. Averaging two class averages is only valid when both classes have the same size; otherwise you need the weighted average, which is the totals method in disguise.
Total distance divided by total time, never the average of the two speeds. When equal distances are covered at two speeds, the result is the harmonic mean, which is why this question is set so often as a trap.
Every question here has been checked against a worked solution before being published, and anything without a complete solution is not shown at all. The bank mixes questions written for CAT-level practice with questions from actual CAT papers; the previous-year questions are collected separately under CAT PYQs. The solutions themselves open in practice mode once you sign up, which is free.