Average- Aptitude Questions and Answers

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The sum of two numbers is 15 and their geometric mean is 20% lower than their arithmetic mean. Find the numbers?

A)

11,4


B)
12,3

C)
13,2

D)
10,5


Correct Answer :

12,3


Explanation :

Let the numbers be x and y.
x+y = 15, or
y = 15 - x ...…(1)
GM= (xy)^1/2
AM = (x+y)/2 = 15/2

As given,
GM = AM - 20% of AM
GM = AM( 1 - 20/100)
(xy)^1/2 = [(x+y)/2]*80/100
(xy)^1/2 = 15/2 * 80/100 = 6
Square both sides

xy =6^2 = 36
y = 36/x ...…(2)

Equate (1) and (2)
15-x = 36/x, or
x^2–15x+36=0
(x-12)(x-3) = 0
So x = 12 or 3 and y = 3 or 12.

So the two numbers are 3 and 12.

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The average salary of the entire staff in a office is 120 rs per month. The average salary of officers is 460 rs and that of non ­officers is 110 rs. If the number of officers is 15, then the number of non ­officers in the office is?

A)
500

B)
488

C)
510

D)
450


Correct Answer :

510


Explanation :

Let the required number of non officers = x
Then, 110*x + 460 * 15 = 120 * ( x + 15 )
or, 120x - 110x = 460 *15 - 120 * 15
10x = 15 *( 460 - 120 )
10x = 15 *340
x = 15*34
So the number of non ­officers in the office is, x = 510

Average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio 2:3, then find the value of the smallest number (between remaining two numbers) ?

A)
36

B)
45

C)
48

D)
54


Correct Answer :

36


Explanation :

Average = Sum of quantities/ Number of quantities
Let the remaining two numbers are 2x and 3x
Then ,Sum of remaining two numbers = Sum of 11 numbers - Sum of 9 numbers
2x+3x = 11*36 - 9*34
5x = 396 - 306
5x= 90
x=18

Therefore,the numbers are 2x=>36 and 3x=>54
the value of the smallest number=>36

The average age of 7 members of Patel's family is 25 year. The average age of the same family 3 year ago was?

A)
21 year

B)
22 year

C)
25 year

D)
24 year


Correct Answer :

22 year


Explanation :

Present average age of family = 25 year
3 year ago average of family = 25 - 3 = 22 years

The average salary of all the 60 employees in an office is Rs 12000 per month. If the number of executives is twice the number of non executives employees, then the average salary of all the non executives employees is ?

A)
Rs. 9000

B)
Rs. 8000

C)
Rs. 6000

D)
Can't be determined


Correct Answer :

Can't be determined


Explanation :

Let the Number of executives be 2X and Number of non-executives be X
As is given, 2X+X=60
X=20
Therefore, Number of executives, 2X = 40 , and number of non-executives employees, X = 20
Now,
Total salary = 40 * salary of executives + 20 * salary of non-executives
60 * 12000 = 40 * k + 20 * l, here k, l are unknowns
so we con't determine the required average salary

The average age of a group of 10 friends is 15 yr. If one friend leaves the group, the average becomes 16 yr. Find the age of the friend who left the group ?

A)
5 yr

B)
4 yr

C)
6 yr

D)
10 yr


Correct Answer :

6 yr


Explanation :

Age of friend left = Previous average of the age - Number of persons present x Increase in average age
= 15 - ( 10-1 ) x ( 16-15 )
= 15- 9 x 1
= 15 - 9 = 6yr

The average age of 24 students in a class is 10. If the teacher’s age is included, the average increase by one . The age of the teacher is ?

A)
25 year

B)
30 year

C)
35 year

D)
40 year


Correct Answer :

35 year


Explanation :

Age of the teacher = Sum of age of 24 students and teacher - Sum of age of 24 students.
= 25 x 11 - 24 x 10
= 35 years.
Thus, Age of teacher = 35 years

The average marks of 30 students are 45 but after checking there are two mistakes found. After adjustment if a student got 45 more markes and other student got 15 less marks, then What will be the adjusted average?

A)
45

B)
44

C)
47

D)
46


Correct Answer :

46


Explanation :

Total number of all students of the class = 30 x 45 = 1350

After adjustment effective increment in marks=45–15=30

New total marks=1350+30=1380

Thus, New average after adjustment=1380/30=46

The average weight of 60 students in a class was calculated to be 40 kg. Later it was found out that the weight of one of the students was calculated as 36 kg, whereas his actual weight was 33 kg. What is the actual average weight of the students in the class ?

A)
39.90 kg

B)
39.95 kg

C)
39 kg

D)
38 kg


Correct Answer :

39.95 kg


Explanation :

Total correct weight = (40 x 60) - 36 + 33 = 2400 - 3 = 2397 kg
Thus, Required average weight = 2397/60 = 39.95 kg

What is the average of the first 6 multiples of 7?

A)
21

B)
28

C)
24.5

D)
25


Correct Answer :

24.5


Explanation :

Required average =7*(1+2+3+4+5+6) / 6
=7*(6*(6+1)/2) /6
=7*42 / 6*2
=24.5

The average of 9 numbers is 18.If the average of first five numbers is 19 and the average of last 5 numbes is 17, find the 5th number?

A)
16

B)
20

C)
18

D)
22


Correct Answer :

18


Explanation :

Let x1, x2, x3, ......., x8, x9 be the numbers

x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9= 18*9
x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9= 162 .... (1)

x1+ x2+ x3+ x4+ x5= 19*5
x1+ x2+ x3+ x4+ x5= 95 ....(2)

x5+ x6+ x7+ x8+ x9= 17*5
x5+ x6+ x7+ x8+ x9= 85 ....(3)

Adding equations (2) and (3) and then subtracting equation (1) from it, we get
x5= 18

Five years ago the average age of four men is 48 years. Now, a new man joins and the average age increases by 2 years. What is the age of the new man?

A)
36 years

B)
42 years

C)
41 years

D)
38 years


Correct Answer :

38 years


Explanation :

Sum of the ages of the four men five year ago= (48 *4) year = 192 year
Present sum of the ages of the four men= 192 + (5* 4) year = 212 year

Now, a new man joins and the average age increases by 2 years = 48+2 =50

So, 50 =(212+ Age of the new man) / 5
Age of the new man = (50* 5)- 212 year = 38 year

The mean yearly salary of employees of a company was 20000. The mean yearly salaries of male and female employees were 20800 and 16800 respectively. Find the ratio of males to females employed by the company?

A)
3 : 2

B)
4 : 1

C)
2 : 1

D)
5 : 3


Correct Answer :

4 : 1


Explanation :

Let the number of males be x and the number of females be y.
Sum of the salaries of the men = 20800x
Sum of the salaries of the females = 16800y
Now, 20000 = 20800x + 16800y / (x + y)
20000 (x + y) = 20800x + 16800y
800x = 3200y
x/y =4/1
x : y = 4 : 1

Average of two numbers is 14.5 and square root of their product is 10. What are the numbers?

A)
16 and 9

B)
25 and 4

C)
4 and 16

D)
25 and 9


Correct Answer :

25 and 4


Explanation :

Let the number be a and b. Then Average is, (a +b) / 2 = 14.5
a + b = 29

as given square root of their product is √ab = 10
ab = 100

(a - b)2 = (a + b)2 - 4ab
(29)2 -(4 *100)= 441
(a - b) = 21
On solving a + b = 29 and a - b = 21, we get a =25 and b = 4.

The average age of a group of four men whose ages are in the ratio 2: 3: 4: 5 is 42 years, what is the age of the eldest person in this group?

A)
60 years

B)
48 years

C)
36 years

D)
24 years


Correct Answer :

60 years


Explanation :

Let the ages of the four men be 2x, 3x, 4x and 5x year respectively.
As given, Sum of ages four men (2x + 3x + 4x + 5x) = 42 * 4
14x = 42 *4
x =168/14 = 12
Hence, the age of the eldest person is, 5x = (5 *12) years = 60 years

If the mean of first n natural numbers is 13 then n=?

A)
26

B)
25

C)
24

D)
20


Correct Answer :

25


Explanation :

Sum of (1 + 2 + 3 +…. + n) =n(n+1)/2

Mean = [n(n+1)/2] / n => (n+1)/2

As given, (n+1)/2 = 13
n+1 =26
n=25

Find the median of the series: 38,28,34,42,50,40,48?

A)
40

B)
48

C)
42

D)
28


Correct Answer :

40


Explanation :

The median of a series of numbers is the number that appears in the middle .
arranged series from smallest to largest => 28,34,38,40,42,48,50

Median =40

Note:If the number of members of the series was even, the average of the two middle numbers would be the median

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