Considering the available options, the dynasty that declined due to the economic interests of Americans and Europeans was the "Quin dynasty."
This is because the Quin dynasty, which lasted between 1644 to 1912, began to have issues with the Europeans, particularly the British, through the trade of Opium in the 19th century
This economic interest from the British led to the Opium War, which devasted the dynasty.
Later the western forces engaged the dynasty in another war in Boxer Rebellion.
Finally, the Quin dynasty fell when western-educated revolutionary Sun Zhongshan formed the Revive China Society at the end of the 19th century, which later led to the end of the Quin dynasty in 1912.
Hence, in this case, it is concluded that the correct answer is option A. "Quin Dynasty."
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