According to Official Guinness Records,
The Katoomba Scenic Railway in Blue Mountains, New South Wales, Australia, has a 52°-angle slope (128% maximum gradient). The 310-m-long (1,017-ft) funicular was originally built for mining purposes in 1878 but was converted into a recreational ride for tourists in 1945.
For a complete list of 1878 records, please visit 1878 Guinness Records in Australia.