Five years ago, karma was one third as old as her father then. in five years, karma will be half as old as her father will be then. find their ages now.

Let X represent Karma's fathers age and Y represent Karma's age. The first term can be found using this formula:

Y = 1/3X  →  5 Years ago
Y = 1/2X  →  5 Years from now

From mental math, I can concur she's 15 and her father is 35. Then we plug in to check.

1/3(30) = 10 √ (Five years ago).
1/2(40) = 20 √ (Five years from current).

Their current ages are 15 and 35.