Person A sees himself as stationary and sees person B moving towards him at half the speed of light

So to person A, time is slowing down for person B and person B is aging slower

When they are 10 light years apart they are both 40 years old

20 years later when person B arrives he is only 50 years old since timed moved slower for him while person A is 60 years old

But person B would see the the same thing, when person A arrives, person A is 50 years old and person person B is 60 years old

They can't both happen, so what would happen?

My guess is that person B would not see the same thing as Person A

When they are 10 light years apart, Person B would see himself as 30 years old, and person A as 50 years old

So 20 years later when Person B got there , he would be 50 years old and person A would be 60 years old

Is this correct?