Problems

On her birthday, my grandma was asked how old she was. She said: "Start with the year I was born. Add the current year to it. Then, from the sum subtract the year I celebrated by \(20\)th birthday. From that, take away the year I was \(30\). The result will be \(16\)." How old is my grandma?

In the long addition above, each letter corresponds to a different digit. What is the sum \(D + O +G + C +A +T\)?