# Averages Problems for SSC CGL

16.

The average age of a group of 10 students was 18. 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.) 15.5
B.) 12.5
C.) 24
D.) 16.5

Answer: Option 'C'

The average age of a group of 10 students is 18.
Therefore, the sum of the ages of all 10 of them = 10 * 18 = 180
When two students joins the group, the average increase by 1.
New Average = 19 Now there are 12 students Therefore, sum of all the ages of 12 students = 228
Therefore, the sum of the ages of two students who joined = 228 - 180 = 48
And the average age of these two students = 24

17.

Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

A.) 2 years
B.) 4 years
C.) 6 years
D.) 8 years

Answer: Option 'C'

Given
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.

18.

Find the average of the first 56 natural numbers

A.) 28.5
B.) 28
C.) 27.5
D.) 29

Answer: Option 'A'

Solution is
Average of the first n natural numbers = (n + 1) / 2
Average of the first 56 natural numbers = (56 + 1) / 2
= 57 / 2
= 28.5

19.

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

Answer: Option 'A'

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

20.

The average of 28 numbers is zero. Of them, at the most how many may be greater than zero?

A.) 27
B.) 28
C.) 29
D.) 26

Answer: Option 'A'

Average of 28 numbers is = 0
Therefore sum of all 28 numbers = 0
It is quite possible that 27 of these numbers may be positive and if their sum is "a" then 28th number is "(-a)"

21.

Total Marks obtained by a class is 3245 and the average score of the class is 55. Find the Total students in the class?

A.) 59
B.) 58
C.) 57
D.) 60

Answer: Option 'A'

Use the below formula to find the Total, when Average and Total No. of Students is provided Total no of students = Total Marks / Average Marks Total No. of students = ( 3245 / 55) = 59

22.

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

Answer: Option 'B'

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

23.

In the first 10 overs of a cricket game, the run rate was only 6.2. What should be the run rate in the remaining 40 overs to reach the target of 414 runs?

A.) 7.92
B.) 8.8
C.) 9.68
D.) 13.09

Answer: Option 'B'

Required Run rate = ( 414 - ( 6.2 x 10 ) )/ (40) = ( 352) /(40) = 8.8

24.

If 13:11 is the ratio of present age of Jothi and Viji respectively and 15:9 is the ratio between Jothi's age 4 years hence and Viji's age 4 years ago. Then what will be the ratio of Jothi's age 4 years ago and Viji's age 4 years hence?

A.) ( 15 : 9)
B.) ( 9 : 5 )
C.) (11 : 13)
D.) ( 12:15)

Answer: Option 'C'

Let the present age of Jothi and Viji be 13X and 11X respectively.
Given, Jothi's age 4 years hence and Viji's age 4 years ago in the ratio 15:9.
That is, (13X + 4) / (11X - 4) = 15 / 9
=> 9 (13X + 4) = 15 (11X - 4)
=> 117X + 36 = 165X - 60
=> 165X - 117X = 60 + 36
=> 48X = 96
=> X = 96 / 48
=> X = 2
Now, Required ratio = (13X - 4) / (11X + 4)
on substituting value of X = 2 we get,
= [13(2)-4] / [11(2)+4]
= 22/26
11/13
Hence the answer is 11:13

25.

The average of 26 numbers is zero. Of them, at the most how many may be greater than zero?

A.) 25
B.) 27
C.) 24
D.) 13

Answer: Option 'A'

Average of 26 numbers is = 0 Therefore sum of all 26 numbers = 0
It is quite possible that 25 of these numbers may be positive and if their sum is "a" then 26th number is "(-a)"

26.

A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A.) 32 years
B.) 36 years
C.) 40 years
D.) 48 years

Answer: Option 'C'

Let the mother's present age be x years.
Then, the person's present age =( 2 / 5years.)
After 8 years, he will be one-half of the age of his mother
=> ( 1 / 2) ( x + 8 )
=> ( 2 / 5 x + 8) = ( 1 / 2 ) ( x + 8)
=> 2( 2 x + 40) = 5 (x + 8)
=> 4 x + 80 = 5x + 40
=> 4x - 5x = 80 - 40
=> x = 40
Present age of Mother = 40 years.

27.

The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?

A.) 42
B.) 57
C.) 27
D.) None of these

Answer: Option 'C'

The total of seven numbers = 7 × 18 = 126
The total of first 3 and last 3 numbers is = 3 × 14+3 × 19 = 99
So, the middle number is (126 - 99 ) = 27

28.

Physics Teacher knows the average score of 59 students in her subject is 49.5. Can you help the physics teacher to find the overall marks obtained by all the students in her subject?

A.) 2774.48
B.) 2920.5
C.) 3212.55
D.) 3066.53

Answer: Option 'B'

Use the below formula to find the Total, when Average and Total No. of Students is provided Total = Average * Total Students/People Total = Average * Total Number of Students) Average Weight = ( 49.5 x 59) = 2920.5

29.

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A.) 20, 35, 45
B.) 16, 28, 36
C.) 10, 25, 35
D.) 8, 20, 28

Answer: Option 'B'

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 => 20x = 80 => x = 4.
Therefore, Their present ages are 4x = 16 years,
7x = 28 years and 9x = 36 years respectively.

30.

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

Answer: Option 'A'

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