Questions for Problems on Ages with Solutions
1. John is twice as old as his sister. If John is 20 years old, how old is his sister?
a) 10
b) 15
c) 20
d) 25
Answer: a) 10
Explanation: If John is 20 years old and he is twice as old as his sister, his sister must be 20 / 2 = 10 years old.
2. The ages of three friends are in the ratio of 3:5:7. The sum of their ages is 60. What is the age of the younger friend?
a) 12
b) 20
c) 25
d) 30
Answer: a) 12
Explanation: Let the ages of the three friends be 3x, 5x, and 7x.
We know that the sum of their ages is 60.
So, we can write: 3x + 5x + 7x = 60
Simplifying this equation, we get: 15x = 60
x = 4
Therefore, the ages of the three friends are:
3x = 12
5x = 20
7x = 28
The three friends are 12 years old, 20 years old, and 28 years old.
Younger friend age = 12 years.
3. The sum of the ages of a father and his son is 52. Five years ago, the father was five times as old as his son. What is the present age of his son?
a) 12
b) 25
c) 30
d) 35
Answer: a) 12
Explanation: Let the father's present age be F and the son's present age be S.
We know that F + S = 52 (since the sum of their ages is 52).
F - 5 = 5 (S - 5)
F - 5 = 5S - 25
F = 5S - 20
Substituting the above in F + S = 52, we get,
5S - 20 + S = 52
6S = 72
S = 12
Therefore, the father's age is F = 52 - 12 = 38.
The son’s age is 12 years.
4. The present age of Tia and Ria is in the ratio of 3:4. Five years back, the ratio of their ages was 2 : 3. What is Tina's present age?
a) 12 years
b) 15 years
c) 20 years
d) 22 years
Answer: b) 15
Explanation: Let the present age of Tia be 3x.
Let the present age of Ria be 4x.
5 years back, Tia’s age = (3x - 5) years
5 years back, Ria’s age = (4x - 5) years
According to the question, (3x - 5) : (4x - 5) = 2 : 3
⇒ (3x - 5) /(4x - 5) = 2/3
⇒ 3 (3x - 5) = 2 (4x - 5)
⇒ 9x - 15 = 8x - 10
⇒ x = 5
Therefore, Tia’s current age = 3 × 5 = 15 years.
5. A father is 45 years old, and his son is 20 years old. In how many years will the father be thrice as old as his son?
a) 7.5
b) 12.5
c) 30
d) 35
Answer: a) 7.5
Explanation: Let x be the number of years in the future. At that time, the father will be 45 + x years old and the son will be 20 + x years old. We know that the father will be thrice as old as his son.
So, (45 + x) = 3 (20 + x)
Solving for x, we get 2x = 15
x = 7.5 years
Therefore, in 7.5 years, the father will be thrice as old as his son.
6. Two brothers are 10 years apart in age. If the older brother is 25, how old is the younger brother?
a) 10
b) 15
c) 20
d) 25
Answer: b) 15
Explanation: The younger brother is 15 years old (25 - 10 = 15).
Additional Questions on Problems on Ages for Practice
1. A grandfather is twice as old as his granddaughter. If the grandfather is 70 years old, how old is the granddaughter?
2. Two brothers have a combined age of 60 years. The elder brother is 4 years older than the younger brother. How old is the elder brother?
3. If the present age of a father is 45 years and the present age of his son is 15 years, what was the father's age when his son was born?
4. If the present age of a grandmother is 65 years and the present age of her granddaughter is 10 years, what will be the age difference between them after 25 years?
5. A father is 50 years old and his son is one-fourth his age. How old is the son?
Answers
1. 35
2. 32
3. 30
4. 55
5. 12.5
