Step-by-step Solution:

Quick Solution

This age puzzle can be solved by translating the given information into a system of two algebraic equations. This will allow us to find their present ages first, and then answer the final question.

1. Set Up the Equations

- Let the Father's present age be F and Rohit's present age be R.

• Clue 1: "Father is aged three times more than the age of his son Rohit." This is a key phrase which means F = R + 3R. This simplifies to:
  F = 4R --- (Equation 1)
• Clue 2: "After 8 yr, he would be two and a half of Rohit's age." (which is 2.5 times).
  In 8 years, their ages will be (F+8) and (R+8). The equation is:
  F + 8 = 2.5 × (R + 8) --- (Equation 2)

2. Find Their Present Ages

- First, substitute Equation 1 into Equation 2 to create an equation with only one variable, R:
(4R) + 8 = 2.5(R + 8)
4R + 8 = 2.5R + 20
4R - 2.5R = 20 - 8
1.5R = 12
R = 8. (Rohit's present age is 8).

- Now, use Rohit's age to find the Father's age using Equation 1:
F = 4 × 8 = 32. (The Father's present age is 32).

3. Answer the Final Question

- The question asks for their age relationship "After further 8 yr". This means we need to look 8 + 8 = 16 years into the future from their present ages.
- Father's age in 16 years = 32 + 16 = 48.
- Rohit's age in 16 years = 8 + 16 = 24.

- To find how many times the father's age would be of Rohit's, we find the ratio of their future ages:
48 ÷ 24 = 2.

Final Answer: After a further 8 years, the father would be 2 times of Rohit's age.