BANK & INSURANCE (AGE BASED PROBLEMS) PART 3

Total Questions: 45

31. In a family, a couple has a son and daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

Correct Answer: (d) 60 years
Solution:

Let the mother age be y years

So, the age of father = (y + 9) years

and, The age of son = y/2 years

ATQ

y + 9 = 3(y/2 − 7)

⇒ y + 9 = (3y − 42)/2

⇒ 2y + 18 = 3y − 42

⇒ y = 60 years

32. A family consists of paternal grandparents, parents and three grandchildren. The average age of the grandparents is 70 years, that of the parents is 40 years and that of the grandchildren is 10 years. What is the average age of the family?

Correct Answer: (b) 35(5/7) years
Solution:

The average age of the grandparents is 70 years.

So, the total age of the grandparents = 70 × 2 = 140 years

The average age of the parents is 40 years.
So, the total age of the parents = 40 × 2 = 80 years

The average age of the grandchildren is 10 years.
So, the total age of the grandchildren = 10 × 3 = 30 years

∴ The total age of the family members = 140 + 80 + 30 = 250 years

∴ The average age of the family = 250 / 7 = 35(5/7)

33. The average age of Manoj and Rima at the time of their marriage was 25 years. A son was born to them two years after their marriage. The present average age of all the three of them is 24 years. How many years is it since the couple got married?

Correct Answer: (d) 8 years
Solution:

Given, average age of Manoj and Rima is 25 years.

⇒ Sum of ages of Manoj and Rima = 50 years

Let the number of years since they got married be x years

Given, child was born after 2 years of marriage

∴ Age of child = (x − 2) years

Now, Sum of ages of three members:

50 + x + x + (x − 2) = 48 + 3x

And, given, present average age of all the three of them is 24 years

So,

48 + 3x = 24 × 3

⇒ 48 + 3x = 72

⇒ 3x = 24

⇒ x = 8 years

34. If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68 and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?

Correct Answer: (d) 12 years
Solution:

P + R + 2Q = 59   …(i)

Q + R + 3P = 68   …(ii)

P + 3Q + 3R = 108  …(iii)

From 3 × (ii) − (iii)

P = 12 years

35. The ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born at the same time when person was died. After another three years, one more member died, again at 60, and a child was born at the same time when person was died. The current average age of this eight-member joint family is nearest to?

Correct Answer: (c) 20 years
Solution:

Total age of family = 231 years

Three years later total age of family

= 231 + 8 × 3 − 60

= 195 years

After another three years total age of family

= 195 − 60 + 8 × 3

= 159 years

Average age ≈ 20 years

36. Ravi has three children: two daughters and one son. All were born on the same date in different years. The sum of the ages of the two daughters today is smaller than the age of the son today, but a year from now the sum of the ages of the daughters will equal the age of the son. Three years from today, the difference between the age of the son and the combined ages of the daughters will be?

Correct Answer: (d) -2
Solution:

One year from now,

D + d = s

two years after that,

D + 2 + d + 2 = s + 2

D − 2 − 4 = −2

37. The average age of board of directors of a company having 15 directors was 48 years. When a director aged 56 resigned from the board of directors another director died on the same day. A new director joined board of directors aged 36. Next year the average age of all 14 directors was found to be 48 years. The age of late director at the time of his death was?

Correct Answer: (b) 42 years
Solution:

Before Death = 48 × 15 = 720

The age of late director at the time of his death

720 − (56 + x) + 36 + 14 = 672

x = 42

38. Eight years ago, Poorvi's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son at that time will be 7:6. If Poorvi's husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter?

Correct Answer: (b) 23 years
Solution:

P − 8 = S + D   — (1)

6D + 30 = 7S + 35 — (2)

H = 7 + P

H = 3S

3S = 7 + P    — (3)

Solving eqn (1), (2) and (3)

D = 23

39. 15 years ago the average age of a family of four members was 40 years. Two children were born in this span of 15 years. The present average of the family remains unchanged. Among the two children who were born during the 15 years, if the older child at present is 8 years older than the younger one, what is the ratio of the present age of the older child to the present age of the younger child?

Correct Answer: (b) 7:3
Solution:

15 years ago Total age of a family of four members = 160

Sum of the Present age of a family of four members = 160 + (15 × 4) = 220

Sum of the Present age of a family of six members = 40 × 6 = 240

x + x + 8 = 20

x = 6

Present age of the older child to the present age of the younger Child

= 14 : 6

= 7 : 3

40. There were 15 students in a class. When the ages of a teacher and a new boy are added, the average age of the class increases by 10 per cent while it remains the same when only the age of a boy is added. If the teacher's age is eight more than twice the age of the new boy, then find the initial average age of the class.

Correct Answer: (c) 11.4 years
Solution:

Let initial average age = x years

After adding age of boy, average remains same

So, boy's age = x years

Therefore, Teacher's age = 2x + 8

According to question,

(15x + x + 2x + 8) / 17 = 1.1x

⇒ 18x + 8 = 18.7x

⇒ x = 11.4 Years (approx.)