Problems on Average with steps -Set 2

 

 Problems on Average with steps -Set 2

11. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. The average age of the family is

A. 32.27 years B. 31.71 years C. 28.17

years D. 30.57 years

Answer : Option B

Explanation :

Total age of the grandparents = 67×2

Total age of the parents = 35×2

Total age of the grandchildren = 6×3

Average age of the family ={

(67×2)+(35×2)+(6×3)}/7=(134+70+18)/

7=222/7=31.71

12. The average weight of A, B and C is 45 kg. If the

average weight of A and B be 40 kg and that of B

and C be 43 kg, what is the weight of B?

A. 31 kg B. 2812 kg C. 32 kg D. 3012 kg

Answer : Option A

Explanation :

Let the weight of A, B and C are a,b and c

respectively.

Average weight of A,B and C =

a+b+c=45×3=135—equation(1)

average weight of A and B = 40

a+b=40×2=80—equation(2)

average weight of B and C = 43

b+c=43×2=86 —equation (3)

equation(2) +equation(3)- equation(1)

=> a+ b+ b +c “(a +b +c)=80+86”135

=>b=80+86"135=166"135=31

=> weight of B = 31

13. If the average marks of three batches of 55, 60

and 45 students respectively is 50, 55, 60, what

is the average marks of all the students?

A. 53.23 B. 54.68 C. 51.33 D. 50

Answer : Option B

Explanation :

Average marks of batch1 = 50

Students in batch1 = 55

Total marks of batch1=55×50

Average marks of batch2 = 55

Students in batch2 = 60

Total marks of batch2=60×55

Average marks of batch3 = 60

Students in batch3 = 45

Total marks of batch3=45×60

Total students = 55 + 60 + 45 = 160

Average marks of all the students

= {(55×50)+(60×55)+(45×60)}/160

= (275+330+270)/16

= 875/16=54.68

14. The average age of husband, wife and their child

3 years ago was 27 years and that of wife and the

child 5 years ago was 20 years. What is the

present age of the husband?

A. 40 B. 32 C. 28 D. 30

Answer : Option A

Explanation :

let the present age of the husband = h

present age of the wife = w

present age of the child = c

3 years ago, average age of husband, wife and

their child = 27

= >Sum of age of husband, wife and their child

before 3 years = 3×27=81

= > (h-3) + (w-3) + (c-3) = 81

= > h + w + c = 81+9 = 90 —————————

equation(1)

5 years ago, average age of wife and child = 20

= >Sum of age of wife and child before 5 years =

2×20=40

= > (w-5) + (c-5) = 40

= > w + c = 40+10 = 50 —————————

equation(2)

Substituting equation(2) in equation(1)

= > h + 50 = 90

= > h = 90 - 50 = 40

= >present age of the husband = 40

15. The average weight of 8 person’s increases by

2.5 kg when a new person comes in place of one

of them weighing 65 kg. What is the weight of the

new person?

A. 70 B. 75 C. 85 D 80

Answer : Option C

Explanation :

Total increase in weight = 8×2.5=20

If x is the weight of the new person, total

increase in weight = x - 65

=> 20 = x - 65

=> x = 20 + 65 = 85