Question

The scale of a map is represented by representative fraction as 1 : 4000. The distance between two points A and B in the map is 10 cm. The distance AB on the ground is (in km units): 
1. 0.04
2. 40
3. 4
4. 0.4

Answer 1

Correct Answer - Option 4 : 0.4

Concept:

Representative factor

• It is a map scale in which figures representing units (as cm, inches, or feet) are expressed in the form of the fraction 1 / x (as 1/250,000) or of the ratio 1 : x to indicate that one unit on the map represents x units (as 250,000 cm) on the earth's surface.
• \({\rm{Representative\;fraction}} = \frac{{{\rm{Map\;distance}}}}{{{\rm{Ground\;distance}}}}\)

​Calculation:

Given,

Representative fraction = 1 : 4000, Map distance = 10 cm

\( \frac{{{\rm{1}}}}{{{\rm{4000}}}}= \frac{{{\rm{10~cm}}}}{{{\rm{Ground\;distance}}}}\)

⇒ Ground distance = 40000 cm = 0.4 km

 The distance AB on the ground is 0.4 km