# Averages Problems for SSC CGL

1.

The average age of a group of 10 students was 22. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

A.) 27
B.) 27.5
C.) 28
D.) 28.5

The average age of a group of 10 students is 22.
Therefore, the sum of the ages of all 10 of them = 10 * 22 = 220
When two students joins the group, the average increase by 1. New Average = 23
Now there are 12 students
Therefore, sum of all the ages of 12 students = 12 X 23 = 276
Therefore, the sum of the ages of two students who joined = 276 - 220 = 56
And the average age of these two students = 28

2.

Of the three numbers whose average is 45, the first is half of the sum of the others. The first number is:

A.) 45
B.) 51
C.) 59
D.) 49

45

3.

The average age of father and his two sons is 27 Years. Five years ago, the average age of the two sons was 12 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?

A.) 42
B.) 47
C.) 48
D.) 49

The total present age of father and two sons is 3S27 = 81 yrs
The total present age of sons is (12+5) X 2 = 34Years
so, present age of father is 81 - 34 = 47 yrs

4.

There were 25 students in a particular Class. The class teacher knows the overall height of all the students in the class is 1400. Can you find the average height of students in the class?

A.) 56
B.) 58.8
C.) 61.6
D.) 53.2

Use the below formula to find the average height of students in the class
Average Height = ( Total Height of all students in the Class / Total Number of Students)
Average Height
= ( 1400 / 25)
= 56

5.

The average age of a group of 10 students was 22. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

A.) 28
B.) 28.7
C.) 30
D.) 32

The average age of a group of 10 students is 22.
Therefore, the sum of the ages of all 10 of them = 10 * 22 = 220
When two students joins the group, the average increase by 1. New Average = 23
Now there are 12 students Therefore, sum of all the ages of 12 students = 12 x 23 = 276
Therefore, the sum of the ages of two students who joined = 276 - 220 = 56
And the average age of these two students = 28

6.

Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59. Then find the seventh result?

A.) 135
B.) 125
C.) 115
D.) 105

Given,Average of 13 results is 65.
Total result = Average * No. of results
=> Total result = 13 x 65 = 845
Given,average of first six results = 61
=> Total of first six = 61 * 6 = 366 and
Given,average of last six results is 59
=> Total for last six = 59 * 6 = 354
Then,
Seventh result = Total result – (Total of first six + Total for last six)
= 845 - ( 366 + 354 )
= 125
Therfore, Seventh result = 125

7.

In the first 35 overs of a cricket game, the run rate was only 6.4. What should be the run rate in the remaining 15 overs to reach the target of 410 runs?

A.) 12.4
B.) 13.4
C.) 15.25
D.) 17.25

Required Run rate = ( 410 - ( 6.4 x 35 ) )/ (15)
= ( 186) /(15) = 12.4

8.

The average mark of 40 students is 45. But after checking, marks of two students were corrected. After correction, if a student got 45 marks more and the other student got 15 marks less, then what will be the adjusted average?

A.) 55.75
B.) 65.75
C.) 45.75
D.) 35.75

Given, Number of students = 40
Average marks of 40 students = 45
=> Total marks of 40 students = Average marks × Number of students
= 45 × 40
1800
Given, After correcting 2 students marks, one student got 45 more marks and other student got 15 less marks
=> After adjustment, Total marks of 40 students = 1800 + 45 - 15
1830

Now, the required Adjusted Average marks= Total marks After adjustment / Number of students
= 1830 / 40
45.75

Therefore, the Adjusted Average marks = 45.75

9.

There were 20 students in a particular Class. The class teacher knows the overall height of all the students in the class is 1400. Can you find the average height of students in the class?

A.) 66.5
B.) 70
C.) 77
D.) 73.5

Use the below formula to find the average height of students in the class Average Height = ( Total Height of all students in the Class / Total Number of Students) Average Height = ( 1400/20) = 70

10.

The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

A.) 20
B.) 20.5
C.) 21.5
D.) 19

The average age of a group of 10 students is 14.
Therefore, the sum of the ages of all 10 of them = 10 * 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students
Therefore, sum of all the ages of 12 students = ( 12 X 15 ) = 180
Therefore, the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students =20

11.

The average of 14 numbers is zero. Of them, at the most how many may be greater than zero ?

A.) 14
B.) 13
C.) 12
D.) 7

Average of 14 numbers is = 0
Therefore sum of all 14 numbers = 0
It is quite possible that 13 of these numbers may be positive and if their sum is "a" then 14th number is "(-a)"

12.

In the first 25 overs of a cricket game, the run rate was only 1.3. What should be the run rate in the remaining 25 overs to reach the target of 287 runs. ?

A.) 10.2
B.) 12.2
C.) 9.2
D.) 14.1

"Required Run rate = ( 287 - ( 1.3 x 25 ) )/ (25) = ( 254.5) /(25) = 10.18 "

13.

In the first 35 overs of a cricket game, the run rate was only 6.4. What should be the run rate in the remaining 15 overs to reach the target of 410 runs. ?

A.) 13.6
B.) 12.4
C.) 11.2
D.) 46.5

"Required Run rate = ( 410 - ( 6.4 x 35 ) )/ (15) = ( 186) /(15) = 12.4 "

14.

The average weight of a class having 25 students is 32 kg. Find the total weight of the class.

A.) 3200
B.) 1600
C.) 1225
D.) 800

Solution is
Given, Average weight = 32 kg
No.of students = 25
Average = Total Quantity / No. of Quantity
=> Total Weight of the class = Average weight x No. of Students
= 32 x 25
= 800

15.

Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result?

A.) 115
B.) 135
C.) 125
D.) 105