Averages Problems for SSC CGL

1.

Total Marks obtained by a class is 1584 and the average score of the class is 72. Find the Total students in the class?  

   A.) 20
   B.) 21
   C.) 22
   D.) 23

Answer: Option 'C'

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
= ( 1584 / 72)
= 22
Total students in class = 22

2.

The average of 8 numbers is zero. Of them, at the most how many may be greater than zero?

   A.) 4
   B.) 6
   C.) 7
   D.) 8

Answer: Option 'C'

Average of 8 numbers is = 0 
Therefore sum of all 8 numbers = 0
It is quite possible that 7 of these numbers may be positive and if their sum is "a" then 8th number is "(-a)".

3.

In a class of 27, the overall weight of the students is 1024. Can you find the average weight of students in the class?

   A.) 37.93
   B.) 41.72
   C.) 39.83
   D.) 36.03

Answer: Option 'A'

Use the below formula to find the average weight of the class Average Weight = ( Total Weight of Class / Total Number of Students) Average Weight = ( 1024/27) = 37.93

4.

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

5.

Total Marks obtained by a class is 1156 and the average score of the class is 68. Find the Total students in the class?

   A.) 16
   B.) 17
   C.) 18
   D.) 19

Answer: Option 'B'

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 = ( 1156 / 68) = 17

6.

The average of marks of a student of 8 exams was 35. How many marks must be get in the next exam so as to increase his average of marks by 5?

   A.) 75
   B.) 80
   C.) 83
   D.) 79

Answer: Option 'B'

80

7.

A particular student has scored an average marks of 69.25 in all his 33 subjects. Find the Total Score he has obtained in all his subjects?

   A.) 2513.78
   B.) 2399.51
   C.) 2170.99
   D.) 2285.25

Answer: Option 'D'

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 = ( 69.25 x 33) = 2285.25

8.

What is the average of first 21 multiples of 7?

   A.) 49
   B.) 77
   C.) 66
   D.) 57

Answer: Option 'B'

Required average  = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 )  (because sum of first 21 natural numbers)
= 77

9.

Find the average of the first 70 natural numbers ?

   A.) 31.5
   B.) 35.5
   C.) 34.5
   D.) 35

Answer: Option 'B'

Solution is :
Average of the first n natural numbers = ( n + 1 ) / 2
Average of the first 70 natural numbers = ( 70 + 1 ) / 2
= 71 / 2
= 35.5

10.

There were 22 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.) 60.46
   B.) 63.64
   C.) 70
   D.) 66.82

Answer: Option 'B'

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 = ( 1400/22) = 63.64

11.

In a class of 27, the overall weight of the students is 743. Can you find the average weight of students in the class?

   A.) 27.52
   B.) 28.9
   C.) 30.27
   D.) 26.14

Answer: Option 'A'

Use the below formula to find the average weight of the class Average Weight = ( Total Weight of Class / Total Number of Students) Average Weight = ( 743/27) = 27.52

12.

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)"

13.

There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess (in Rs)?

   A.) 562
   B.) 585
   C.) 548
   D.) 650

Answer: Option 'B'

Let the original expenditure be Rs.x
Original average expenditure = X/45
New average expenditure = (x+39)/52
So (x/45) - ((x+39) / 52) = 1 => (52x - 45x - 45 × 39) / (45 × 52) = 1 => (7x - 1755) / 2340 = 1 => 7x = 2340 + 1755 => 7x = 4095 so x = 585
so, original expenditure is Rs 585

14.

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

Answer: Option 'A'

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

15.

Physics Teacher knows the average score of 43 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.) 2341.35
   B.) 2234.93
   C.) 2128.5
   D.) 2022.08

Answer: Option 'C'

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 43) = 2128.5

16.

Total Marks obtained by a class is 864 and the average score of the class is 72. Find the Total students in the class?

   A.) 10
   B.) 11
   C.) 12
   D.) 13

Answer: Option 'C'

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 = ( 864 / 72) = 12

17.

The average temperature for Monday, Tuesday and Wednesday is 36.30 C. The average temperature for Tuesday, Wednesday and Thursday is 36.70 C. If Monday's temperature recorded as 390 C, find the Thursday's temperature ?

   A.) 40.2º C
   B.) 40.4º C
   C.) 40.5º C
   D.) 41.2º C

Answer: Option 'A'

Mon + Tue + Wed Temperature = 3X36.3 = 108.9
Given, Monday's temperature = 39º C
=> Tue + wed Temperature = 108.9 - 39 = 69.9
Given, Tue + wed + Thu temperature = 3 X 36.7 = 110.1
So, Thursday's temperature = 110.1 - 69.9 = 40.2º C

18.

In the first 30 overs of a cricket game, the run rate was only 1.9. What should be the run rate in the remaining 20 overs to reach the target of 98 runs. ?

   A.) 2.3
   B.) 2.5
   C.) 2.1
   D.) 8.5

Answer: Option 'C'

"Required Run rate = ( 98 - ( 1.9 x 30 ) )/ (20) = ( 41) /(20) = 2.05 "

19.

In the first 25 overs of a cricket game, the run rate was only 5.6. What should be the run rate in the remaining 25 overs to reach the target of 280 runs. ?

   A.) 6.16
   B.) 6.72
   C.) 5.6
   D.) 5.04

Answer: Option 'C'

Required Run rate = ( 280 - ( 5.6 x 25 ) )/ (25) = ( 140) /(25) = 5.6

20.

The average temperature for Monday, Tuesday and Wednsday is 36.3 degrees C. The average temperature for Tuesday, Wednesday and Thursday is 36.7 degrees C. if Monday's temperature recorded as 39 degrees c, find the Thursday's temperature ? 

   A.) 40.2º C
   B.) 40.4º C
   C.) 41.4º C
   D.) 39.2º C

Answer: Option 'A'

MOn + Tue + wed Temperature  =  3 × 36.3 = 108.9
Tue + wed Temperature = 108.9 - 39 = 69.9
Tue + wed + Thu temperature = 3 × 36.7 = 110.1
So, Thursday's temperature = 110.1 - 69.9 = 40.2º C

21.

Total marks obtained by a class is 720 and the average score of the class is 72. Find the total number of students in the class? 

   A.) 11
   B.) 10
   C.) 12
   D.) 13

Answer: Option 'B'

Total number of students = Total Marks / Average Marks
Total No. of students = (720 / 72) = 10

22.

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.) 10.18
   B.) 9.162
   C.) 12.216
   D.) 14.058

Answer: Option 'A'

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

23.

Total Marks obtained by a class is 3685 and the average score of the class is 55. Find the Total students in the class?

   A.) 65
   B.) 66
   C.) 67
   D.) 68

Answer: Option 'C'

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 = ( 3685 / 55) = 67

24.

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

   A.) 6.3
   B.) 6.5
   C.) 7.3
   D.) 8.3

Answer: Option 'A'

Required Run rate = ( 282 - ( 3.2 x 10 ) ) / (40) = ( 250) / (40) = 6.25

25.

Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is: 

   A.) 15
   B.) 21
   C.) 17
   D.) 18

Answer: Option 'D'

Let first number be x. 
So,2nd no. = 4x & 3rd no.=8x.
So,x+4x+8x=78 × 3 = 234.
13x = 234 
x = 234/13 
Hence,smallest Number x=18.


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