SQL: Top (Latest) Item Per Group

I spent far too long this morning on trying to find a solution to this SQL problem.
Consider the PERSON table:

Location Name Age
London Fred 45
London Mark 35
London Mike 25
Cardiff Jim 56
Cardiff Julia 46
Cardiff Murray 36
Edinburgh Sheila 61
Edinburgh Launa 51
Edinburgh Lin 41

Suppose you want the name of the oldest person at each location. How do you achieve this in SQL?

Like this:

The result should be:

Location Name Age
London Fred 45
Cardiff Jim 56
Edinburgh Sheila 61

Thanks to Findy Services and B. Jacobs for this solution.