# Averages ( 6 to 10 )

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Averages ( 6 to 10 ):

# APTITUDE QUESTIONS (AVERAGES):

6. If the average marks of three batches of 55, 60 and 45 students respectively are 50, 55 and 60, then the average marks of all the students is:

A)    53.33

B)    54.68

C)    55

D)    60

E)    None of these

Explanation:

Required Average = [ (55*50+60*55+45*60)/(55+60+45) ]= (2750+3300+2700)/160 = 8750/160 = 54.68

7. Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is:

A)    15

B)    45

C)    48

D)    60.25

E)    None of these

Explanation:

Le the first number be x.
Then, the sum of the four numbers = x + 4x = 5x.
So, 5x/4 =60 or x = (60*4)/5=48

8. If the arithmetic mean of seventy-five numbers is calculated, it is 35. If every number is increased by 10, then the mean of new numbers is:

A)    45

B)    30

C)    70

D)    90

E)    None of these

Explanation:

Arithmetic Mean of 75 numbers = 35
The sum of 75 numbers = (75 * 35) = 2625
Total increase = (75 * 10) = 750
Increased sum = (2625 + 750) = 3375
Increased average = 3375/75}=45

9. The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is:

A)    7

B)    19

C)    82

D)    84

E)    None of these

Explanation:

Average of 10 numbers = 7
The sum of these 10 numbers is = (10 * 7) = 70
∴ x1 + x2 + ……+ x10 = 70
=> 12×1 + 12×2 + ……+ 12×10 = 840
=> (12×1 + 12×2 + … + 12×10)/10}=84
=> Average of new numbers is 84.

10. The average number of 11 numbers is 10.9. The average of the first 8 numbers is 10.5 and that of the last 8 numbers is 11.4, then what is the middle number:

A)    51

B)    41.3

C)    51.4

D)    55.3

E)    None of these