BANK & INSURANCE (AVERAGE) PART 3

Total Questions: 45

11. The average age of 6 children of a family is 12 years. If the age of their mother and father is also added, then the average age of whole family becomes 27 years. If the age of the father is 8 years more than that of the age of the mother, then find the age of the mother?

Correct Answer: (b) 68 years 
Solution:

Sum of the age of children is = 6 × 12
⇒ 72 years

Now, Let the age of the father is = F years
And the age of the mother is = M years

Then, according to the question,
= 72 + F + M = 27 × 8
⇒ 72 + F + M = 216
⇒ F + M = 216 - 72
⇒ F + M = 144 (i):

And, the age of the father is = F = M + 8
⇒ F - M = 8 (ii): Solving both equation we get,
F + M = 144
F - M = 8
⇒ 2F = 152
⇒ F = 76 years

So, the age of the mother is = 76 - 8 ⇒ 68 years
Hence, the required answer is = 68 years.

12. Total number of men and women is 80, they are collecting fruits. Average number of fruits collected by men in an half hour is 30 and the average number of fruits collected by women in 120 minutes is 88. If the average number of fruits collected by all the 80 persons in 60 minutes is 50, then find the number of women in the group?

Correct Answer: (d) 50 
Solution:

Number of men = x
Number of women = 80 - x

Number of fruits collected by men in 60 minutes
= 30 × x × 2 = 60x

Total number of fruits collected by women in 60 minutes
= 88 × (80 - x)/(120/60) = 44 × (80 - x):

Total number of fruits collected by all the persons in 60 minutes = 50 × 80 = 4000

60x + 44 × (80 - x) = 4000
60x + 3520 - 44x = 4000
x = 30

Number of women = 80 - 30 = 50

13. If 7 employees whose average age is 35 years are added in the company, the average age of the company is decreased by 4.2 years. If 7 employees whose average age is 35 years are removed from the company, the average age of the company is increased by 7 years, then what is the initial average age of the company?

Correct Answer: (c) 56 years
Solution:

Total number of employees in the company = x
Initial average age of the company = y

(xy + 7 × 35)/(x + 7) = y - 4.2
xy + 245 = xy - 4.2x + 7y - 29.4
7y - 4.2x = 274.4 ---- (1)

(xy - 7 × 35)/(x - 7) = y + 7
xy - 245 = xy + 7x - 7y - 49
7y - 7x = 196
y - x = 28 ---- (2)

From (1) and (2): 2.8x = 78.4
x = 28
y = 56

14. The average age of the company is 48 years and the total number of employees in the company is 30. If the ratio of the male to female employees in the company is 3: 2 and the average age of the female employees in the company is 52.5 years, then what is the average age of the male employees in the company?

Correct Answer: (c) 45 years
Solution:

Total age of the company = 48 × 30 = 1440
Number of male employees in the company = 3/5 × 30 = 18
Number of female employees in the company = 2/5 × 30 = 12

Total age of female employees = 52.5 × 12 = 630
Total age of male = 1440 - 630 = 810
Average age of male employees = 810/18
= 45 years

15. Four years ago the average age of the class is 24 years. Two years ago one student left the class with age of 29 years and after one year the new student joined the class with the age of 24 years. If the initial number of students from the class is 16, then find the present approximate average age of the class?

Correct Answer: (a) 27.6 years  
Solution:

Four years ago the total age of the class = 24 × 16 = 384
Two years ago the total age of the class = 384 + 16 × 2 - 29 = 387

One year ago the total age of the class = 387 + 24 + 15 = 426
Present age of all the students = 426 + 16 = 442
Average age = 442 / 16 = 27.625 years

16. The average weight of the first eight students is 150kg, the average weight of the last ten students is 10 more than the average weight of first eight students. The average weight of the rest two students is 300 kg. The average weight of all the students is __ years. Then the 40% of the weight of all the students is __ years.

Correct Answer: (d) 170 kg and 68 kg
Solution:

Sum of the weight of the first eight students
= 150 × 8 = 1200
Sum of the weight of the last ten students is
= (150 + 10) × 10
= 160 × 10 = 1600

Average weight of rest of two students = 300
So, the sum of the last two students is = 300 × 2 = 600

So, the sum of weight of all students is
= 1200 + 1600 + 600 = 3400

So, the average weight of all the students is
= 3400/20 = 170 kg

Then the 40% weight of all students
= 170 × 40/100 = 68 kg

Hence the required answer is = 170 kg and 68 kg.

17. There are 30 students in a class whose average age is 20 years. The average age of boys in a class is 3 less than average age of girls in it. If the age of their class teacher, which is between 49 to 54 years is included with boys, the average of boys becomes equal to that of girls. If average age of boys as well as girls are integers, then how many boys are there in class?

Correct Answer: (c) 10
Solution:

Let the number of boys in a class be a, and their average age is b years. Let the age of teacher is c years.
Sum of ages of all students in the class = 30 × 20 = 600 years

So, a × b + (30 - a) × (b + 3) = 600
So, a × b + 30b + 90 - a × b - 3a = 600
So, a = 10b - 170 ........ (1)

When teacher is also included
So, (a × b + c)/(a + 1) = b + 3
So, a × b + c = a × b + 3a + b + 3
So, c = 3a + b + 3 ........ (2)

Put value of b in equation 2 from equation 1
c = 3a + (a + 170)/10 + 3
c = 31a/10 + 20

But a, should be an integral value
Put a = 10
Then c = 31 × 10/10 + 20 = 51

Put a = 20
Then, c = 31 × 20/10 + 20 = 82 (not possible)

C is the age of teacher which is between 49 and 54 years.
So only possible value of a = 10

18. Ratio of average weight of children and men in a family is 3:5 and average weight of women is 54 kg. Number of children in the family is 60% of number of men and number of women in the family is 20% more than the number of men. Find the ratio of total weights of men, women and children in that family respectively if average weight of men is 60 kg.

Correct Answer: (c) 25:27:9
Solution:

Let number of man in a family = 5a
Number of children in a family = 60% of 5a = 3a
Number of woman in a family = 120% of 5a = 6a

Average weight of children = 3/5 × 60 = 36 kg

Required ratio = (5a × 60) : (6a × 54) : (3a × 36)
= 25 : 27 : 9

19. There are seven members in the group A, B, C, D, E, F and G and the average age of these seven members is 16(1/7) years. Sum of the ages of A and F is 3 years more than C and C is 28 years elder than G. If the sum of the ages of E and D is 18 years less than C and the present age of B is 28 years, then what is the average age of C and G?

Correct Answer: (c) 18 years
Solution:

A + B + C + D + E + F + G = 113/7 × 7 = 113
A + F = C + 3
C - G = 28
E + D = C - 18
B = 28

C + 3 + 28 + C + C - 18 + C - 28 = 113
4C = 128
C = 32 years
G = 4 years

Required average = (32 + 4)/2
= 18 years

20. In a class, there are 25 students and the average weight of the class is 18 kg. If the average weight of class is increased by 2 years, when two new students S1 and S2 are added to the class and the weight of S1 is 22.22% more than the weight of S2, then find the weight of S1?

Correct Answer: (c) 49.5 kg
Solution:

Let the weight of S2 = 9x
And the weight of S1 = 9x × 11/9 = 11x

The total weight of S1 and S2 = 27 × 20 - 25 × 18 = 90 kg
9x + 11x = 90
x = 90/20 = 4.5

The weight of S1 = 11 × 4.5 = 49.5 kg