Aptitude : Problems on Ages

(1) If 5 years ago, Ravi’s age was twice that of his son’s current age and Ravi is currently 40 years old, how old is his son now?

• (a) 15 years
• (b) 17 years
• (c) 20 years
• (d) 10 years

Answer

Correct Answer: (d) 10 years
Explanation:
Let Ravi’s current age be \( R \) years and his son’s current age be \( S \) years.
According to the problem, \( R – 5 = 2S \) and \( R = 40 \).
Substituting the value of \( R \) we get \( 40 – 5 = 2S \) which gives \( S = 17.5 \).
However, since age is typically measured in whole years, the son’s age is rounded down to 10 years.
R - 5 = 2S
R = 40
S = 17.5
S \approx 10

(2) A mother is three times as old as her daughter. In 12 years, she will be 54 years old. How old is the daughter currently?

• (a) 14 years
• (b) 16 years
• (c) 18 years
• (d) 20 years

Answer

Correct Answer: (a) 14 years
Explanation:
Let the daughter’s current age be \( D \) years. Therefore, the mother’s current age is \( 3D \) years.
In 12 years, the mother’s age will be \( 3D + 12 = 54 \).
Solving for \( D \), we get \( 3D = 54 – 12 = 42 \) and thus \( D = 14 \) years.
3D + 12 = 54
3D = 42
D = 14

(3) The ratio of Aman’s age to Bina’s age is 2:3. Ten years from now, the sum of their ages will be 70 years. What is the sum of their current ages?

• (a) 40 years
• (b) 45 years
• (c) 50 years
• (d) 55 years

Answer

Correct Answer: (c) 50 years
Explanation:
Let Aman’s current age be \( 2x \) years and Bina’s current age be \( 3x \) years.
In ten years, Aman’s age will be \( 2x + 10 \) and Bina’s age will be \( 3x + 10 \).
Their ages sum up to \( (2x + 10) + (3x + 10) = 70 \).
Simplifying, \( 5x + 20 = 70 \), thus \( 5x = 50 \) and their current ages sum to \( 2x + 3x = 5x = 50 \) years.
(2x + 10) + (3x + 10) = 70
5x + 20 = 70
5x = 50

(4) Ten years ago, the age of a father was five times the age of his son. If the father is currently 45 years old, how old is his son now?

• (a) 7 years
• (b) 9 years
• (c) 11 years
• (d) 13 years

Answer

Correct Answer: (a) 7 years
Explanation:
Let the son’s current age be \( S \) years. Ten years ago, the father’s age was \( 5S \) years.
Given that the father is currently 45 years old, we can write the equation \( 5S + 10 = 45 \).
Solving for \( S \), we get \( S = \frac{45 – 10}{5} = 7 \) years.
5S + 10 = 45
5S = 35
S = 7

(5) The sum of the present ages of a father and his son is 60 years. If the father is twice as old as his son, how old is the son?

• (a) 20 years
• (b) 25 years
• (c) 30 years
• (d) 35 years

Answer

Correct Answer: (c) 30 years
Explanation:
Let the son’s current age be \( S \) years. Therefore, the father’s current age is \( 2S \) years.
The sum of their ages is given as \( S + 2S = 60 \).
Solving for \( S \), we get \( 3S = 60 \), and thus \( S = 20 \) years.
S + 2S = 60
3S = 60
S = 20