The youngest Prime Minister to be appointed was William Pitt the Younger on 19 December 1783 at the age of 24 years, 6 months and 21 days.
Explanation:
William Pitt the Younger (28 May 1759 – 23 January 1806) was a prominent British Tory statesman of the late eighteenth and early nineteenth centuries. He became the youngest prime minister of Great Britain in 1783 at the age of 24 and the first prime minister of the United Kingdom of Great Britain and Ireland as of January 1801. He left office in March 1801, but served as prime minister again from 1804 until his death in 1806. He was also Chancellor of the Exchequer for all of his time as prime minister. He is known as "the Younger" to distinguish him from his father, William Pitt, 1st Earl of Chatham, who is customarily referred to as "William Pitt the Elder" (or less commonly, simply "Chatham") and had previously served as prime minister.
