BANK & INSURANCE (AGE BASED PROBLEMS) PART 1

Total Questions: 45

31. Three years ago the average age of A and B was 18 years. While C joining them now, the average becomes 22 years. How old (in years) is C now?

Correct Answer: (a) 24
Solution:

Three years ago,

The sum of the age of A and B

= 18 × 2 = 36 years

∴ Sum of the present age of A and B

= 36 + 6 = 42 years

Sum of the present age of A, B and C

= 3 × 22 = 66 years

∴ present age of C = 66 − 42 = 24 years

32. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Correct Answer: (b) 16, 28, 36
Solution:

Let the 3 persons be A, B and C.

Given: The ratio of the present ages of 3 persons is 4 : 7 : 9

Let the present age of A, B and C be 4x, 7x and 9x years respectively.

A : B : C ⇒ 4x : 7x : 9x

Given, 8 years ago, the sum of their ages was 56.

8 years ago, the ratio of the ages is

A : B : C ⇒ 4x − 8 : 7x − 8 : 9x − 8

Given, the sum of the above ages was 56.

4x − 8 + 7x − 8 + 9x − 8 = 56

⇒ 20x − 24 = 56

⇒ 20x = 56 + 24

⇒ 20x = 80

⇒ x = 4

So, present ages of A, B and C be 4 × 4, 7 × 4, 9 × 4

i.e. 16, 28 and 36 respectively.

33. The sum of present ages of father and his son is 57 years. 6 years ago, the father was 4 times as old as his son at that time. The present age of son is?

Correct Answer: (c) 15 years
Solution:

Let son's present age = p years

Therefore, Present age of father = (57 − p) years

ATQ

(57 − p − 6) = 4(p − 6)

51 − p = 4p − 24

p = 15 years

34. The difference between the present ages of Arun and Deepak is 14 years. Seven years ago, the ratio of their ages was 5:7 respectively. What is Deepak's present age?

Correct Answer: (e) None of these
Solution:

Seven years ago,

Let Arun's and Deepak's age be 5x and 7x years respectively.

∴ Arun's Present age = (5x + 7) years

Deepak's Present age = (7x + 7) years

According to the question,

7x + 7 − 5x − 7 = 14

⇒ 2x = 14

⇒ x = 7

∴ Deepak's present age = 7x + 7

= 7 × 7 + 7 = 56 years

35. The present ages of three colleagues are in proportions 3 : 5 : 7. Four years ago, the sum of their ages was 48. find their present ages (in years)?

Correct Answer: (a) 12, 20 and 28 years
Solution:

Let the present age of three colleagues are : 3x, 5x and 7x

(3x − 4) + (5x − 4) + (7x − 4) = 48

15x − 12 = 48 ⇒ 15x = 60 ⇒ x = 4

Their present ages are 12 years, 20 years and 28 years respectively.

36. One year ago, the ratio of Gaurav's and Sachin's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Sachin?

Correct Answer: (b) 36 years
Solution:

Let Gaurav's and Sachin's ages one year ago be 6x and 7x years respectively.

Then, Gaurav's age 4 years hence

= (6x + 1) + 4 = (6x + 5) years.

Sachin's age 4 years hence

= (7x + 1) + 4 = (7x + 5) years.

(6x + 5) : (7x + 5) = 7 : 8

⇒ 8(6x + 5) = 7(7x + 5)

⇒ 48x + 40 = 49x + 35

⇒ x = 5

Hence, Sachin's present age = (7x + 1) = 36 years

37. Abhay's age after six years will be three-seventh of his father's age. Ten years ago, the ratio of their ages was 1:5. What is Abhay's father's age at present?

Correct Answer: (c) 50 years
Solution:

Let the ages of Abhay and his father 10 years ago be x and 5x years respectively.

Then, Abhay's age after 6 years = (x + 10) + 6 = (x + 16) years.

Father's age after 6 years = (5x + 10) + 6 = (5x + 16) years.

Then,

(x + 16) : (5x + 16) = 3 : 7

⇒ 7(x + 16) = 3(5x + 16)

⇒ 7x + 112 = 15x + 48

⇒ 8x = 64

⇒ x = 8

Hence, Abhay's father's present age

= (5x + 10) = 50 years

38. The ratio of the mother's age to her daughter's age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be?

Correct Answer: (d) 5 : 3
Solution:

Let the present ages of Mother and daughter be 9x and 5x respectively.

9x × 5x = 1125

⇒ 45x² = 1125

⇒ x² = 25

⇒ x = 5

Required ratio = (9x + 5) : (5x + 5)

⇒ 50 : 30

⇒ 5 : 3

39. The ratio of the present ages of two Friends is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years?

Correct Answer: (b) 3 : 4
Solution:

Let the present ages of the two Friends be 2x and 3x respectively.

Then,
(2x−6)/(3x−6) = 1/3

⇒ 6x − 18 = 3x − 6 ⇒ 3x = 12 ⇒ x = 4.

So, required ratio = (2x + 4) : (3x + 4)

⇒ 12 : 16 ⇒ 3 : 4.

40. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is?

Correct Answer: (b) 7 : 3
Solution:

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then,

(3x + 10) + 10 = 2[(x + 10) + 10]

⇒ 3x + 20 = 2x + 40

⇒ x = 20.

∴ Required ratio = (3x + 10) : (x + 10)

= 70 : 30 = 7 : 3.