How old is Scrooge in DuckTales (2017)?
Kids who read the original Carl Barks Donald Duck and Uncle Scrooge comic books back in the 1940s, 1950s, and 1960s may have noticed that Scrooge McDuck sometimes mentioned various previous adventures looking for treasure around the world. Adventures that meant that Scrooge was at least as old as the parents of those kids and the grandparents of those kids and even the great grandparents of those kids - 1950s kids who are now old enough to have grandchildren and sometimes great grandchilden.
Don Rosa, the greatest of Carl Barks's successors as Duck artist, actually compiled a biography, The Life and Times of Scrooge McDuck (1992-1996). According to Rosa, Scrooge was born in Glasgow, Scotland in 1867, and met Donald Duck and Huey, Dewey, and Louie, in 1947 in "Christmas at Bear Mountain", having all of his Carl Barks adventures afterwards.
Don Rosa also believed that Scrooge died in 1967 aged 100, though that was never made official, and set all his Scrooge stories before 1967. And to get Scrooge McDuke to live "only" 100 years Don Rosa had to change or ignore a few of Bark's dates. Rosa lists the few Barks stories or plot details he ignored or changed for the Life and Times of Scrooge McDuck here:
http://stp.lingfil.uu.se/~starback/dcml/creators/rosa-on-himself.html#dates
see the heading The Life and Times of Scrooge McDuck (Lo$, 12-part series)
According to Wikipedia:
"According to Carl Barks' 1955 one-pager "Watt an Occasion" (Uncle Scrooge #12), Scrooge is 75 years of age. According to Don Rosa, Scrooge was born in Scotland in 1867, and earned his Number One Dime (or First Coin) exactly ten years later. The DuckTales episodes (and many European comics) show a Scrooge who hailed from Scotland in the 19th century, yet was clearly familiar with all the technology and amenities of the 1980s. Despite this extremely advanced age, Scrooge does not appear to be on the verge of dotage, and is vigorous enough to keep up with his nephews in adventures; with rare exception there appears to be no sign of him slowing down."
"Barks responded to some fan letters asking about Scrooge's Adamic age, that in the story "That's No Fable!", when Scrooge drank water from a Fountain of Youth for several days, rather than making him young again (bodily contact with the water was required for that), ingesting the water rejuvenated his body and cured him of his rheumatia, which arguably allowed Scrooge to live beyond his expected years with no sign of slowdown or senility. Don Rosa's solution to the issue of Scrooge's age is that he set all of his stories in the 1950s or earlier, which was when he himself discovered and reveled in Barks's stories as a kid, and in his unofficial timelines, he had Scrooge die in 1967, at the age of 100 years."
https://en.wikipedia.org/wiki/Scrooge_McDuck#Age
So Rosa and Bark's versions of Uncle Scrooge were really old coots, even if Scrooge was not a member of the Coot family like his in law Elvira Coot (Grandma Duck).
So if the "present" in DuckTales (2017) is near the present date of 2018, and if Scrooge was born as early as Rosa claimed, Scrooge McDuck's birthday in "McMystery at McDuck McManor!", May 25, 2018, could be his 149th or 150th or 151st!
In the DuckTales episode "The impossible Summit of Mount Neverrest", December 2, 2017, Scrooge attempts to climb the never climbed Mount Neverrest, and admits to his nephews that he was the legendary "Neverrest Ninny" who failed 75 years earlier. Scrooge and his guide George Mallardy attempted the climb to celebrate Scrooge making his first million dollars. So if Scrooge was already an adult 75 years earlier he should be at least 95 in the episode.
The Klondike Gold Rush in the Yukon region of Canada happened in 1896 to 1899 in real history, and Barks and Rosa used the real historic dates for Scrooge's past adventures. According to stories in The Life and Times of Scrooge McDuke, Scrooge prospected for gold in the Klondike in 1896 to 1898, tangled with Goldie O'Gilt, and struck it rich.
And in the latest Duck Tale "The Golden Lagoon of White Agony Plains", June 23, 2018, Goldie O'Gilt returns to Scrooge's life and they seek a treasure they could never find back in their Klondike prospecting days. At one point Goldie uses a phone to take a picture, a use of current technology. They mention that it is over a hundred years since they tangled in the Klondike, which thus makes Scrooge at least 120 years old in the episode.
A Scrooge old enough to prospect in the Klondike by 1899 would be at least 120 in "The Golden Lagoon of White Agony Plains", and would turn 150 in 2017 if born when Rosa said, or maybe at least about 160 if all of Bark's dates are correct.
So it is probably understandable why the writers of "The Golden Lagoon of White Agony Plains" had Scrooge and Goldie explain to each other that they had stayed young by the use of varous mystical methods!