Ages - Solved Questions and Answers

Problems on Ages are quantitative aptitude questions that involve calculating the current, past, or future ages of individuals based on given relationships and time intervals. 

Problems on Ages questions and answers are provided below for you to learn and practice.

Question 1: A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

Solution: 

Let A’s present age be ‘n’ years.
According to the question,
n + 15 = 5 (n – 5)
=> n + 15 = 5 n – 25
=> 4n = 40
=> n = 10
=> A’s present age = 10 years
Therefore, A’s age 3 years hence = 10 + 3 = 13 years

Question 2: The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?

Solution: 

Let A’s present age be x years. Then, B’s present age = 240 / x years
So, according to question
2 (240 / x ) – x = 4
=> 480 – x² = 4 x
=> x² + 4 x – 480 = 0
=> (x + 24) (x – 20) = 0
=> x = 20
=> B’s present age = 240 / 20 = 12 years
Thus, B’s age 2 years ago = 12 – 2 = 10 years

Question 3: The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, the mother’s age will be 10 years more than twice the age of the daughter. Find the present age of the mother.

Solution: 

Let the daughter’s present age be ‘n’ years.
=> Mother’s present age = (3n + 3) years
So, according to the question
(3n + 3 + 3) = 2 (n + 3) + 10
=> 3n + 6 = 2n + 16
=> n = 10
Hence, mother’s present age = (3n + 3) = ((3 x 10) + 3) years = 33 years

Question 4: The ratio of present ages of A and B is 6 : 7. Five years hence, this ratio would become 7 : 8. Find the present age of A and B.

Solution: 

Let the common ratio be ‘n’.
=> A’s present age = 6 n years
=> B’s present age = 7 n years
So, according to the question
(6 n + 5) / (7 n + 5) = 7 / 8
=> 48 n + 40 = 49 n + 35
=> n = 5
Thus, A’s present age = 6 n = 30 years
B’s present age = 7 n = 35 years

Question 5: A father is currently three times as old as his son. Five years ago, he was four times as old as his son. Find the current ages of the father and the son.

Solution:

Let the son’s current age be x.
Then, the father’s current age is 3x.

Five years ago:

Son’s age = x − 5
Father’s age = 3x − 5

According to the problem, five years ago, the father was four times as old as the son: 3x − 5 = 4(x − 5)

Solve for x: 3x − 5 = 4x − 20 ⇒ x = 15

Current ages:

Son’s age = 15 years
Father’s age = 3 × 15 = 45 years

Therefore, the son is 15 years old, and the father is 45 years old.

Question 6: The age of a man is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children at that time. Find the present age of the man.

Solution:

Let the present age of the man be x years, and the sum of the ages of his two children be y years.

Given:

The man's age is twice the sum of his children's ages:

x = 2y (1)

Also given:
20 years from now, the man's age will equal the sum of his children's ages at that time.

In 20 years:

• Man's age = x + 20
• Each child will be 20 years older, so total = y + 40

So,

x + 20 = y + 40

Substitute equation (1) into this:

2y + 20 = y + 40

Solving:

2y − y = 40 − 20 ⇒ y = 20

Then from equation (1):

x = 2y = 2 × 20 = 40

Therefore, the man's present age is 40 years.

Question 7: The sum of the ages of two siblings is 30 years. Five years ago, the older sibling was twice as old as the younger sibling. What are their current ages?

Solution:

Let older = x , younger = y.

1. x + y = 30

2. x - 5 = 2(y - 5)

From (1), x = 30 - y . Substitute into (2):

30 - y - 5 = 2(y - 5) → 25 - y = 2y - 10

Solve for y : 35 = 3y → y = 35/3= 11.67

Then, x = 30 - 11.67 = 18.33

So, the younger sibling and older sibling current age is 11.67 and 18.33 .

Question 8: The sum of the present age of a father and his daughter is 60 years. Five years ago, the father was five times as old as the daughter. What is the present age of the father?

Solution:

Let the daughter’s present age be x.
Then, the father’s present age = 60 - x
Five years ago:
Father’s age =60 - x - 5 = 55 - x
Daughter’s age = x−5
According to the question:

55 - x = 5(x - 5)

Solving for x:

55 - x = 5x - 25 \Rightarrow 80 = 6x \Rightarrow x = \frac{80}{6} \approx 13.33

So, the daughter is approximately 13.33 years old, and the father is 60 - 13.33 = 46.67 years old.