Let x = A's age now
y = B's age now
A's age in ten years = 2(B's age in ten years).
So, x + 10 = 2(y + 10)
A's age 5 years ago = 3(B's age 5 years ago)
So, x - 5 = 3(y - 5)
We have: x + 10 = 2y + 20
and x - 5 = 3y - 15
Subtracting the equations, we get 15 = -y + 35.
So, y = 20
Substituting for y into x + 10 = 2y + 20
we obtain x + 10 = 60. Therefore, x = 50.
Answer: A is 50 years old and B is 20 years old