Step-by-step explanation:
Let the son's present age be x years
[tex] \therefore [/tex] Father's present age = (x + 22) years.
Four years after:
Son's age = (x + 4)
Father's age = (x + 22 + 4) =(x + 26) years.
According to the given condition:
Father's age = 3 times the son's age
[tex] \therefore \: x + 26 = 3(x + 4) \\ \therefore \: x + 26 = 3x + 12 \\ \therefore \: 26 - 12= 3x - x \\ \therefore \: 14= 2 x \\ \therefore \: x = \frac{14}{2} \\ \huge \red{ \boxed{ \therefore \: x = 7}} \\ \\ \implies \: x + 22 = 7 + 22 \\ \huge\red{ \boxed{ \therefore \:( x + 22)= 29}}[/tex]
Hence, now :
Father's age = 29 years
Son's age = 7 years.
Let us move to the next part of the question:
Let y years ago father's age was 12 times his son.
y years ago
son's age = (7 - y) years
Father's age = (29 - y) years
[tex] \therefore\: 29 - y = 12(7 - y)
\\\\
\therefore\: 29 - y = 84 - 12y
\\\\
\therefore\: 12 y - y = 84 - 29\\\\
\therefore\: 11y = 55\\\\
\therefore\: y = \frac{55}{11}\\\\
\huge\orange{\boxed {\therefore\: y = 5}} [/tex]
Thus, 5 years ago father's age was 12 times than his son.
