Aptitude : Problems on Ages

(6) Five years ago, John was three times as old as David. If John’s current age is 35 years, how old is David now?

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

Answer

Correct Answer: (b) 15 years
Explanation:
Let David’s current age be \( D \) years. Five years ago, John’s age was \( 3D \) years.
Given that John is currently 35 years old, we can write the equation \( 3D + 5 = 35 \).
Solving for \( D \), we get \( D = \frac{35 – 5}{3} = 10 \) years.
3D + 5 = 35
3D = 30
D = 10

(7) The ratio of the present ages of Alice and Bob is 5:7. If the sum of their ages is 72 years, how old is Alice?

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

Answer

Correct Answer: (a) 20 years
Explanation:
Let the present age of Alice be \( 5x \) years and the present age of Bob be \( 7x \) years.
The sum of their ages is given as \( 5x + 7x = 72 \).
Solving for \( x \), we get \( 12x = 72 \), and thus \( x = 6 \).
Alice’s age is \( 5x = 5 \cdot 6 = 30 \) years.
5x + 7x = 72
12x = 72
x = 6
Alice's\ age = 5x = 5 \cdot 6 = 30

(8) A family consists of a grandfather, his son, and his grandson. The sum of their ages is 105 years. If the grandson is 5 years old, how old is the grandfather?

• (a) 65 years
• (b) 70 years
• (c) 75 years
• (d) 80 years

Answer

Correct Answer: (c) 75 years
Explanation:
Let the age of the grandson be \( G \) years. The age of the son is \( 2G \) years, and the age of the grandfather is \( 3G \) years.
Given that the grandson is 5 years old, we can write the equation \( G + 2G + 3G = 105 \).
Solving for \( G \), we get \( G = 15 \) years.
The age of the grandfather is \( 3G = 3 \cdot 15 = 45 \) years.
G + 2G + 3G = 105
6G = 105
G = 15
Grandfather's\ age = 3G = 3 \cdot 15 = 45

(9) Five years ago, the sum of the ages of Alice and Bob was 30 years. If Alice’s current age is twice that of Bob, how old is Bob now?

• (a) 10 years
• (b) 12 years
• (c) 15 years
• (d) 18 years

Answer

Correct Answer: (a) 10 years
Explanation:
Let Bob’s current age be \( B \) years. Five years ago, Alice’s age was \( 2B \) years.
Given that the sum of their ages five years ago was 30 years, we can write the equation \( 2B + B + 10 = 30 \).
Solving for \( B \), we get \( B = 10 \) years.
2B + B + 10 = 30
3B + 10 = 30
3B = 20
B = 10

(10) A man is 5 times as old as his son. If the sum of their ages is 42 years, how old is the son?

• (a) 6 years
• (b) 7 years
• (c) 8 years
• (d) 9 years

Answer

Correct Answer: (d) 9 years
Explanation:
Let the son’s current age be \( S \) years. Therefore, the man’s current age is \( 5S \) years.
The sum of their ages is given as \( S + 5S = 42 \).
Solving for \( S \), we get \( 6S = 42 \), and thus \( S = 7 \) years.
S + 5S = 42
6S = 42
S = 7