Who bought Central Asia Russia or China?
The Russians conquered the Central Asian khanates piecemeal during the 19th century.
Genghis Khan about 800 years ago. People paid in blood. It was expensive, and painful.
Nobody "bought" large parts of central Asia. Russians and Chinese people and Mongols and several other groups invaded much of Asia as various times in the last 3,000 years. The history of that part of the world has been one of fairly continual change. For that matter, so has the history of almost all parts of the world. A large land purchase FROM Russia was Alaska by the USA in the late 1860s. Earlier the USA made the "Louisiana Purchase" from France, which expanded the territories of the USA hugely (far more than the present state of Louisiana). Such large purchases of huge land areas are almost unique in the history of mankind.