Ages - Solved Questions and Answers

Last Updated : 25 Jun, 2025

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 sons. Five years ago, his age was four times the sum of their ages at that time. Find the man’s present age if the sum of the sons’ ages is currently 20 years.

Solution:

Let the current sum of the sons’ ages be 20 years.
The man’s current age = 2 × 20 = 40 years.
Five years ago:
Sons’ total age = 20 − 2 × 5 = 10 years
Man’s age = 40 − 5 = 35 years
According to the problem, five years ago, the man’s age was four times the sons’ total age at that time: 35 = 4 × 10 (This confirms our calculation.)
Therefore, the man’s present age is 40 years.

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