The present age of a father is square of the age of his son. After six years, the age of the father would be 3$$\frac{1}{2}$$​ times the age of the son. The present age of the father is 

Correct option is A

Given:
Present age of father = (son's present age)²
After 6 years, father's age = 3½ times son's age after 6 years
Formula:
Father's present age = (Son's present age)²
After 6 years: (Father's age + 6) = (7/2) × (Son's age + 6)

Solution:

Let present age of son = x years
Then, father's present age = x² years

After 6 years:
Father’s age = x² + 6
Son’s age = x + 6

Given:
x² + 6 = (7/2)(x + 6)

Multiply both sides by 2 to remove the fraction:
2(x² + 6) = 7(x + 6)

Expand:
2x² + 12 = 7x + 42

Rearranging:
2x² - 7x + 12 - 42 = 0
2x² - 7x - 30 = 0

Now, checking the options:

Option (a) 36:
Son’s age = √36 = 6 years
Father’s present age = 36 years

After 6 years:
Father = 36 + 6 = 42 years
Son = 6 + 6 = 12 years

Check the ratio:
42 ÷ 12 = 3.5 = 7/2

Matches perfectly!
Thus, present age of father = 36 years.

Final Answer: (a) 36