The actual distance between the two cities is 200 km. What will be the distance between them on a map with a scale of 1cm:100 km?

Given, the actual distance between the cities = 200 km 
The scale used in the map=1cm: 100km
The distance between the map can be expressed as:
= Scale X Actual size
= $\frac{1}{100 }\times 200 = 2 \mathrm{cm}$ = 10 cm

Therefore, the distance between the two cities will be 2 cm on the map.