Aptitude : Problems on Ages

(25) The sum of the present ages of Jim and his father is 75 years. If Jim’s age is three times that of his father, how old is Jim?

• (a) 15 years
• (b) 18 years
• (c) 21 years
• (d) 24 years

Answer

Correct Answer: (b) 18 years
Explanation:
Let Jim’s current age be \( J \) years and his father’s current age be \( F \) years.
Given that the sum of their ages is 75 years, we can write the equation \( J + F = 75 \).
Also, Jim’s age is three times that of his father, so \( J = 3F \).
We can now solve these equations simultaneously. Substituting \( J = 3F \) into \( J + F = 75 \), we get \( 3F + F = 75 \), which simplifies to \( 4F = 75 \).
Solving for \( F \), we find \( F = 18 \) years. Therefore, Jim’s age is \( J = 3F = 3 \cdot 18 = 54 \) years.

(26) The sum of the ages of a father and his daughter is 44 years. If the father is 28 years older than his daughter, how old is the daughter?

• (a) 8 years
• (b) 12 years
• (c) 16 years
• (d) 20 years

Answer

Correct Answer: (a) 8 years
Explanation:
Let the daughter’s age be \( D \) years. Therefore, the father’s age is \( D + 28 \) years.
The sum of their ages is given as \( D + (D + 28) = 44 \).
Simplifying, \( 2D + 28 = 44 \), and solving for \( D \), we get \( D = 8 \) years.

(27) A woman is three times as old as her niece. If the sum of their ages is 48 years, how old is the niece?

• (a) 12 years
• (b) 16 years
• (c) 18 years
• (d) 20 years

Answer

Correct Answer: (a) 12 years
Explanation:
Let the niece’s age be \( N \) years. Therefore, the woman’s age is \( 3N \) years.
The sum of their ages is given as \( N + 3N = 4N = 48 \).
Solving for \( N \), we get \( N = 12 \) years.

(28) Two years ago, the age of a man was seven times the age of his son. If the man’s current age is 36 years, how old is his son now?

• (a) 4 years
• (b) 6 years
• (c) 8 years
• (d) 10 years

Answer

Correct Answer: (c) 8 years
Explanation:
Let the son’s age be \( S \) years. Two years ago, the man’s age was \( 7S \) years.
Given that the man is currently 36 years old, we can write the equation \( 7S + 2 = 36 \).
Solving for \( S \), we get \( S = \frac{36 – 2}{7} = 5 \) years. Therefore, the son’s age is \( 5 + 2 = 7 \) years.

(29) The sum of the ages of a group of friends is 72 years. If two of them are 16 years old and 22 years old, how old is the third friend?

• (a) 24 years
• (b) 26 years
• (c) 34 years
• (d) 42 years

Answer

Correct Answer: (c) 34 years
Explanation:
Let the age of the third friend be \( T \) years. The sum of their ages is given as \( 16 + 22 + T = 72 \).
Solving for \( T \), we get \( T = 72 – 16 – 22 = 34 \) years.

(30) A father’s age is four times the age of his son. If the father is currently 36 years old, how old is his son now?

• (a) 9 years
• (b) 12 years
• (c) 15 years
• (d) 18 years

Answer

Correct Answer: (a) 9 years
Explanation:
Let the son’s age be \( S \) years. Therefore, the father’s age is \( 4S \) years.
Given that the father is currently 36 years old, we can write the equation \( 4S = 36 \).
Solving for \( S \), we get \( S = \frac{36}{4} = 9 \) years.