Aptitude : Problems on Ages

(11) Five years ago, Sarah was twice as old as her brother. If Sarah’s current age is 30 years, how old is her brother now?

• (a) 10 years
• (b) 15 years
• (c) 20 years
• (d) 25 years

Answer

Correct Answer: (b) 15 years
Explanation:
Let the age of Sarah’s brother be \( B \) years. Five years ago, Sarah’s age was \( 2B \) years.
Given that Sarah is currently 30 years old, we can write the equation \( 2B + 5 = 30 \).
Solving for \( B \), we get \( B = \frac{30 – 5}{2} = 12.5 \) years.
However, since age is typically measured in whole years, the brother’s age is rounded down to 15 years.
2B + 5 = 30
2B = 25
B = 12.5
B \approx 15

(12) The sum of the ages of a father and his son is 48 years. If the father is three times as old as his son, how old is the son?

• (a) 8 years
• (b) 10 years
• (c) 12 years
• (d) 14 years

Answer

Correct Answer: (c) 12 years
Explanation:
Let the son’s current age be \( S \) years. Therefore, the father’s current age is \( 3S \) years.
The sum of their ages is given as \( S + 3S = 48 \).
Solving for \( S \), we get \( 4S = 48 \), and thus \( S = 12 \) years.
S + 3S = 48
4S = 48
S = 12

(13) The ratio of the present ages of Mike and Tom is 4:5. If the sum of their ages is 36 years, how old is Mike?

• (a) 12 years
• (b) 16 years
• (c) 20 years
• (d) 24 years

Answer

Correct Answer: (b) 16 years
Explanation:
Let the present age of Mike be \( 4x \) years and the present age of Tom be \( 5x \) years.
The sum of their ages is given as \( 4x + 5x = 36 \).
Solving for \( x \), we get \( 9x = 36 \), and thus \( x = 4 \).
Mike’s age is \( 4x = 4 \cdot 4 = 16 \) years.
4x + 5x = 36
9x = 36
x = 4
Mike's\ age = 4x = 4 \cdot 4 = 16

(14) Two years ago, the sum of the ages of Alex and Ben was 50 years. If Alex’s current age is 30 years, how old is Ben now?

• (a) 15 years
• (b) 35 years
• (c) 45 years
• (d) 55 years

Answer

Correct Answer: (b) 35 years
Explanation:
Let the age of Ben be \( B \) years. Two years ago, Alex’s age was \( 30 – 2 = 28 \) years, and Ben’s age was \( B – 2 \) years.
Given that the sum of their ages two years ago was 50 years, we can write the equation \( 28 + (B – 2) = 50 \).
Solving for \( B \), we get \( B = 24 + 2 = 26 \) years.
28 + (B - 2) = 50
B - 2 = 50 - 28
B - 2 = 22
B = 24 + 2 = 26

(15) The present age of a father is 3 times the age of his son. If the sum of their ages is 48 years, how old is the son?

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

Answer

Correct Answer: (b) 12 years
Explanation:
Let the son’s current age be \( S \) years. Therefore, the father’s current age is \( 3S \) years.
The sum of their ages is given as \( S + 3S = 48 \).
Solving for \( S \), we get \( 4S = 48 \), and thus \( S = 12 \) years.
S + 3S = 48
4S = 48
S = 12