Question: Which countries found economic growth while cog-railways were built in the Alps?

Knowledge 1: Alps
The tourism industry began in the early 19th century when foreigners visited the Alps, traveled to the bases of the mountains to enjoy the scenery, and stayed at the spa-resorts. Large hotels were built during the Belle Époque; cog-railways, built early in the 20th century, brought tourists to ever higher elevations, with the Jungfraubahn terminating at the Jungfraujoch, well above the eternal snow-line, after going through a tunnel in Eiger. During this period winter sports were slowly introduced: in 1882 the first figure skating championship was held in St. Moritz, and downhill skiing became a popular sport with English visitors early in the 20th century, as the first ski-lift was installed in 1908 above Grindelwald. [SEP] Knowledge 2: Great power
Over time, the relative power of these five nations fluctuated, which by the dawn of the 20th century had served to create an entirely different balance of power. Some, such as the United Kingdom and Prussia (as the founder of the newly formed German state), experienced continued economic growth and political power. Others, such as Russia and Austria-Hungary, stagnated. At the same time, other states were emerging and expanding in power, largely through the process of industrialization. These countries seeking to attain great power status were: Italy after the Risorgimento, Japan after the Meiji Restoration, and the United States after its civil war. By the dawn of the 20th century, the balance of world power had changed substantially since the Congress of Vienna. The Eight-Nation Alliance was a belligerent alliance of eight nations against the Boxer Rebellion in China. It formed in 1900 and consisted of the five Congress powers plus Italy, Japan, and the United States, representing the great powers at the beginning of 20th century.
Knowledge 1: Alps
The region is serviced by 4,200 km (2,600 mi) of roads used by 6 million vehicles. Train travel is well established in the Alps, with, for instance 120 km (75 mi) of track for every 1,000 km2 (390 sq mi) in a country such as Switzerland. Most of Europe's highest railways are located there. Moreover, plans are underway to build a 57 km (35 mi)-long sub-alpine tunnel connecting the older Lötschberg and Gotthard tunnels built in the 19th century. [SEP] Knowledge 2: Great power
Over time, the relative power of these five nations fluctuated, which by the dawn of the 20th century had served to create an entirely different balance of power. Some, such as the United Kingdom and Prussia (as the founder of the newly formed German state), experienced continued economic growth and political power. Others, such as Russia and Austria-Hungary, stagnated. At the same time, other states were emerging and expanding in power, largely through the process of industrialization. These countries seeking to attain great power status were: Italy after the Risorgimento, Japan after the Meiji Restoration, and the United States after its civil war. By the dawn of the 20th century, the balance of world power had changed substantially since the Congress of Vienna. The Eight-Nation Alliance was a belligerent alliance of eight nations against the Boxer Rebellion in China. It formed in 1900 and consisted of the five Congress powers plus Italy, Japan, and the United States, representing the great powers at the beginning of 20th century.
Knowledge 1: Alps
The tourism industry began in the early 19th century when foreigners visited the Alps, traveled to the bases of the mountains to enjoy the scenery, and stayed at the spa-resorts. Large hotels were built during the Belle Époque; cog-railways, built early in the 20th century, brought tourists to ever higher elevations, with the Jungfraubahn terminating at the Jungfraujoch, well above the eternal snow-line, after going through a tunnel in Eiger. During this period winter sports were slowly introduced: in 1882 the first figure skating championship was held in St. Moritz, and downhill skiing became a popular sport with English visitors early in the 20th century, as the first ski-lift was installed in 1908 above Grindelwald. [SEP] Knowledge 2: Economic inequality
Some theories developed in the 1970s established possible avenues through which inequality may have a positive effect on economic development. According to a 1955 review, savings by the wealthy, if these increase with inequality, were thought to offset reduced consumer demand. A 2013 report on Nigeria suggests that growth has risen with increased income inequality. Some theories popular from the 1950s to 2011 incorrectly stated that inequality had a positive effect on economic development. Analyses based on comparing yearly equality figures to yearly growth rates were misleading because it takes several years for effects to manifest as changes to economic growth. IMF economists found a strong association between lower levels of inequality in developing countries and sustained periods of economic growth. Developing countries with high inequality have "succeeded in initiating growth at high rates for a few years" but "longer growth spells are robustly associated with more equality in the income distribution."

Answer: United Kingdom and Prussia