-  Let the present ages of father and son be X and Y years, respectively
Then, (X - 1) = 4(Y -1)
or,       4Y - X = 3                   …..(1)
And,    (X + 6) - 2(Y + 6) = 9
or,       -2Y + X = 15              …..(2)
Solving (1) and (2), we get , X = 33, Y = 9
Ratio of their ages = 33 : 9 = 11 :3

Let the age of father be ‘x’ years and that of son be ‘y’ years.

Given:
One year ago, father’s age = x
One year ago, son’s age = y

Therefore, x - 1 = 4(y - 1)
=> x – 4y = -3 ……….(1)

Also, it is given that in 6 years time, father’s age will exceed twice the son’s age by 9 years.

Let us assume the age of father and son after 6 years be x + 6 and y + 6 respectively.

Therefore, x + 6 = 2(y + 6) + 9
=> x + 6 = 2y + 21 ……….(2)

Solving equations (1) and (2), we get
x = 11 and y = 3

Therefore, ratio of father’s age to son’s age = 11 : 3

Hence, the correct option is C.

If you think the solution is wrong then please provide your own solution below in the comments section .