Age Mystery

An old man was playing with his grandson before the boy started asking about their ages.

Boy: Grandpa, what will happen to our ages 7 years from now?
Grandpa: The sum of our ages will be a perfect square.

Boy: Oh, and then what will happen 7 years after that?
Grandpa: Then the ratio of my age to yours will be a perfect square.

Boy: Really? At that time will our ages combine to become 100?
Grandpa: No, my boy, but if we add your present age to the sum of our ages in 14 years, then it will be 100.

What is the sum of their present ages?


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