Average
Average
Average Aptitude Concepts and Formulas
Points to remember:
1) The average of n quantities of the same kind is equal to the sum of all the quantities divided by the number of quantities;
Average =
Sum of quantities = Average ∗ Number of quantities
Number of quantities =
2) Average of two or more than two groups;
If the number of quantities in two groups are n_{1} and n_{2} respectively and their individual average is X and Y respectively, the combined average of the two groups is given by;
=
3) If the average of n_{1} quantities is X and the average of n_{2} quantities out of n_{1} quantities is Y, the average of the remaining quantities is given by;
=
4) The average of n quantities is equal to X. One quantity of value P is replaced with a new quantity having value Q the average of quantities becomes Y. Then Q is given by;
Q = P+n (YX)
5) The average of n quantities is equal to X. If we remove one quantity the average becomes Y, the value of the removed quantity is given by;
= n(X – Y) + Y
And, if the average of n quantities is equal to X and on adding a new quantity the average becomes Y, the value of new quantity is given by;
= n ( Y – X) + Y
6) Average of numbers:
1) Natural numbers:

 The average of first n consecutive natural numbers is given by; =
 The average of square of first n consecutive natural numbers is given by; =
 The average of cubes of first n consecutive natural numbers is given by; =
2) Even numbers:

 The average of first n consecutive even numbers is given by;
= n + 1  Also, the average of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;
=
 The average of first n consecutive even numbers is given by;

 The average of square of first n consecutive even numbers is given by;
=
 The average of square of first n consecutive even numbers is given by;
 Also, the average of square of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;
=
3) Odd numbers:

 The average of first n consecutive odd numbers is equal to n.
 Also, the average of first n consecutive odd numbers starting from 1 to X, where the last odd number is X is given by;
=

 The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by;
=
 The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by;
Some quicker methods:
 The average of n numbers is X. If each number is multiplied by Y, the new average is given by;
= Initial average ∗ Y  The average age of a group of boys is given. If the new average age after a boy joins the group is also given, the age of new boy is given by;
Age of new boy = New average + number of boys initially ∗ increase in average  The average weight of a group of persons is given. If we replace a person in the group with another person and the new average is increased,
The weight of new person = weight of the removed person + no. of persons ∗ increase in average.  The average of the marks obtained by students is given. The average of marks obtained by the passed students and failed students are also given, thenNumber of passed candidates =
And, Number of failed students =
1) What is the average of first five multiples of 12?
 36
 38
 40
 42
2) Average of five numbers is 20. If each number is multiplied by 2, what will be the new average?
 30
 40
 50
 60
3) If the average of three consecutive even numbers is 34, find the largest of these numbers.
 30
 32
 34
 36
4) 10 typists can type 600 pages in 8 hours.Find the average number of pages typed by each typist in an hour.
 7 pages
 7.5 pages
 8 pages
 8.5 pages
5) The average of Sohan’s marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?
 94
 92
 90
 88
6) Average age of a group of 30 boys is 16 years. A boy of age 19 leaves the group and a new boy joins the group. If the new average age of the group is 15.8 years, find the age of the new boy.
 12 years
 13 years
 14 years
 15 years
7) The average weight of 10 men is decreased by 2 kg when one of them whose weight is 60 kg is replaced by a new man. What is the weight of the new man?
 35 kg
 40 kg
 45 kg
 50 kg
8) The average age of 30 boys in a class is 15 years. If we include the age of two teachers the average age increases by 1. Find the sum of ages of the two teachers.
 55 years
 58 years
 62 years
 64 years
9) The average age of the committee of 10 members is 40 years. A member of age 52 retires and a new member of age 38 takes his place. What is the average age of the present committee?
 38.6 years
 33.5 years
 35.5 years
 37.5 years
10) Four years ago, the average age of A and B was 20 years. If today average age of A, B and C is 25 years, what will be age of C after 7 years?
 32 years
 34 years
 36 years
 38 years
11) What is the average of first five natural numbers?
 5
 2
 3
 4
12) If the sum is 240 and average is 40, find the number of quantities.
 5
 8
 5
 6
13) A group consists of two male, two female and three children. The average age of the male is 67 years, that of the female is 35 years, and that of the children is six years. What is the average age of the group?
 30.71
 31.71
 28.71
 35.45
14) Mohan gets a salary of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 months. How much salary he must have in the sixth month so that he gets an average of Rs. 6500?
 4091
 4991
 3499
 3344
15) If the average of 20 numbers is zero, how many numbers may be greater than zero?
 19
 49
 17
 33
16) The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.
 20
 85
 67
 80
17) The captain of a cricket team of 11 members is 26 years old, and the wicketkeeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?
 19
 49
 17
 23
18) The average monthly income of Rakesh and Suresh is Rs. 5050. The average monthly income of Suresh and Ramesh is Rs. 6250 and the average monthly income of Rakesh and Ramesh is Rs. 5200. What is the monthly income of Rakesh?
 3000
 6000
 4000
 2500
 30
 40
 60
 25
20) In Varun’s opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Varun, and he thinks that Varun’s weight is greater than 60 kg but less than 70 kg. His sister’s view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Varun?
 60
 65
 67
 54
19) Three years ago, the average age of Anita, Priya, and Varsha was 27 years. If five years ago, the average age of Priya and Varsha was 20 years, find the present age of Anita.
21) The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?
 32
 65
 67
 31
22) The average weight of 16 students in a class is 50.25 kg, and that of the remaining 8 students is 45.15 kg. Find the average weight of all the students in the class.
 34.56
 56.23
 48.55
 31.44
23) A museum has an average of 510 visitors on Sunday and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday.
 285
 275
 237
 245
24) If the average marks of three classes of 45, 60 and 55 students are 60, 55, 50 respectively, find the average marks of all the students.
 52.85
 45.75
 64.68
 54.68
25) In a class average age of 15 boys is 11. If 5 boys each of age 9 years are added, what would be the new average?
 20 years
 10 years
 10.5 years
 23 years
26) If the number of quantities in group A is 10 and in group B is 8, and their individual average is 24 and 16 respectively, find the combined average of the two groups.
 20.44
 18.22
 16.22
 18.66
27) The average of square of first 6 consecutive even numbers is:
 12.20
 60.66
 16.45
 178
28) Find the average of first 4 consecutive even numbers.
 2
 5
 1
 8
29) Find the average of first 5 consecutive even numbers starting from 2 to 10, where the last even number is 10.
 1
 6
 2
 8
30) Find the average of the square of first 6 consecutive even numbers starting from 2 to 12, where the last even number is 12.
 12.20
 60.66
 16.45
 178
31) Find the average of first 20 consecutive natural numbers.
 12.20
 10.78
 16.45
 10.5
32) Find the average of square of first 5 consecutive natural numbers.
 12
 10
 16
 11
33) Find the average of cubes of first 7 consecutive natural numbers.
 112
 110
 116
 113
34) Find the average of first 8 consecutive odd numbers.
 11
 10
 8
 12
35) Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.
 22
 11
 16
 33
36) The average age of a group of 6 boys is 19. If the new average age after a boy joins the group is 21.28, find the age of new boy.
 Approx 23
 Approx 32
 Approx 35
 Approx 45
37) The average weight of a group of 5 boys is 26. If we replace a boy of weight 25 in the group with another boy so that new average increases by 3, find the weight of the new body.
 56
 34
 40
 33
38) Find the average of first 6 consecutive even numbers.
 6
 4
 0
 7
39) Find the average of first 9 consecutive odd numbers.
 9
 4
 0
 7
Leave a Reply
Want to join the discussion?Feel free to contribute!