correct answer is: c) 45 years & 10 years

Explanation

Let, father’s present age is ‘x’ .
\therefore Five years ago, father’s age was =\left(x-5\right)
\therefore Five years hence, father’s age will =\left(x+5\right)
And, Son’s present age is ‘y’ .
\therefore Five years ago, son’s age was =\left(y-5\right)
\therefore Five years hence, son’s age will =\left(y+5\right)
In 1 ^st case,
\left(x-5\right)=8\times\left(y-5\right)
\rightarrow x-5=8y-40
\rightarrow x=8y-40+5
\rightarrow x=\left(8y-35\right)
In 2 ^nd case,
\left(x+5\right)+\left(y+5\right)=65
\rightarrow x+y+10=65
\rightarrow x+y=65-10
\rightarrow x+y=55
\rightarrow x=\left(55-y\right)
According to the question.
\left(8y-35\right)=\left(55-y\right)
\rightarrow8y+y=\left(55+35\right) _{[interchange]}
\rightarrow9y=90
\rightarrow y=\large\frac{90}{9}
\rightarrow y=10
\therefore x=\left(55-10\right) _{[from 2nd case]}
\rightarrow x=45
\therefore Father’s present age is 45 years.
And, Son’s present age is 10 years.
Ans: Their present ages are 45 years & 10 years.

Another form of this specific question exists:

1. What are the current ages of a father and his son if the father’s age was eight times that of his son’s age five years ago, and their combined ages will be 65 years in five years?
2. If the father’s age was eight times his son’s age five years ago, and the sum of their ages will be 65 years in five years, what are their present ages?
3. Find out the current ages of a father and his son if, five years ago, the father’s age was eight times the son’s age, and in five years, their combined ages will be 65 years.