Bob and John form a team together. Bob is as old as John will be when Bob is twice as old as John was when Bob was half as old as the sum of their current ages. John is as old as Bob was when John was half as old as he will become over ten years. How old are Bob and John?

Let Bob's age = B and John's age = J. Solving the complex system of equations yields B = 40 and J = 30. The second statement gives us the key equation: J = (B/2) + 10, which with B = 40 gives J = 30. This pair satisfies the conditions of both statements. Option A (35, 45) and Option C (40, 50) don't satisfy the second condition, while Option D has ages in the wrong order.