Question

6 years hence, Ravi will be twice as old as his son. 18 years ago, Ravi was six times of his son’s age. Find their present ages.

Answer 1

Given:

• 6 years hence, Ravi will be twice as old as his son.
• 18 years ago, Ravi was six times as old as his son.

Step-wise calculation:

1. Let the present age of Ravi be (x) years and the present age of his son be (y) years.

2. According to the first condition 6 years hence: 

x + 6 = 2(y + 6) which simplifies to x + 6 = 2y + 12

⇒ x – 2y = 6

3. According to the second condition 18 years ago:

x – 18 = 6(y – 18) which simplifies to x – 18 = 6y – 108

⇒ x – 6y = –90

4. Now, solve the system of equations:

x – 2⁢y = 6

x – 6y = –90

Subtract the second equation from the first:

(x – 2y) – (x – 6y) = 6 – (–90) 

–2y + 6y = 96 

4y = 96

⇒ y = 24

Substitute (y = 24) into the first equation:

x – 2(24) = 6

⇒ x – 48 = 6

⇒ x = 54

Present age of Ravi is 54 years.

Present age of his son is 24 years.