Aman is six times as old as his son. in nine years, he will be three times as old as his son. how old are they now?

His son is 15 now, and the father is 45.

First, make an equation system based on the problem
For an instance, m stands for the man's age, and s stands for the son's age
"A man is six times as old as his son" could be written as:
⇒ m = 6s (equation 1)
"In nine years, he will be three times as old as his son" could be written as:
⇒ m + 9 = 3(s + 9) (equation 2)

Second, solve the equation system
Substitute 6s to m in equation 1 to equation 2 in order to find the value of s
m + 9 = 3(s + 9)
6s + 9 = 3(s + 9)
6s + 9 = 3s + 27
6s - 3s = 27 - 9
3s = 18
  s = 18/3
  s = 6
The son's age is 6 yo.

Substitute 6 to find m
m = 6s
m = 6(6)
m = 36
The man's age is 36 yo.