India does have some entries here, which have even been cited in the Guinness Book of Records.
http://www.guinnessworldrecords.com/world-records/oldest-appointed-prime-minister
So Morarji Desai (81) is the oldest to be elected Prime Minister for the first time. The case of Philippe Petain (84) is different as he was appointed “Chief of State” and not elected. This appointment came when France was about to be taken over by the invading German forces.
LK Advani (born November 1927) is now 90+ and may have hopes of surpassing Morarjibhai’s record.
There are, of course, others like Mahathir Mohamad who have been elected prime minister (but not for the first time) at a greater age. Other examples include William Gladstone of Britain (82+ when he became PM for the fourth time) and Ronald Reagan (73+ when he was elected President for the second time).
The oldest to become PM of Britain for the first time was Viscount Palmerston (70+) in 1855. India’s war of independence occurred during his first tenure of 1855-58. The change to direct rule in India came during the short tenure of his successor (The Earl of Derby) in 1858-59. Palmerston returned for his second term which was in 1859-1865.
The oldest to become President of the US for the first time is Donald Trump (70+). Incidentally, he, Bill Clinton and George Bush (Jr) were all born in 1946.
These links may be useful:
https://en.wikipedia.org/wiki/List_of_Prime_Ministers_of_the_United_Kingdom_by_age
https://en.wikipedia.org/wiki/List_of_presidents_of_the_United_States_by_age
https://en.wikipedia.org/wiki/List_of_Prime_Ministers_of_India_by_longevity
Contrary to popular belief, Gulzarilal Nanda had a longer lifespan than Morarji Desai. Both crossed 99. (But Morarji Desai celebrated his birthday only in leap years, which is another matter).
Alec Douglas-Home was among the longest-lived Prime Ministers of Britain, though also among the most obscure of those who served in the 20th century.
He was the only British PM to have played first-class cricket. He did not do too well, but at least had better figures than Nawaz Sharif.
abn397 