Draw a graphical scale for the map depicted in a scale of 1 ∶ 50,000 and read the distances in kilometers.

The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. There are at least three ways in which this relationship can be expressed. These are:

1. Statement of Scale
2. Representative Fraction (R. F.)
3. Graphical Scale

Representative Fraction (R.F.): A method of the scale of a map or plan expressed as a fraction showing the ratio between a unit distance on the map or plan, and the distance measured in the same units on the ground

Denominator: The number below the line in a fraction. For example, in a fraction of 1: 50,000; 50,000 is the denominator.

Numerator: The number above the line in a fraction. For example, in a fraction of 1: 50,000, 1 is the numerator.

By convention, a length of nearly 15 cm is taken to draw a graphical scale.

To get the length of line for the graphical scale, these steps may be followed:

• 1: 50,000 means that
• 1 unit of the map represents 50,000 units on the ground
• or 1 cm represents 50,000 cm
• or 15 cm represents 50,000 × 15/100,000 km
• or 15 cm represents 7.5 km

Since the value of 7.5 (km) is not a round number, we can choose 5 or 10 (km) as the round number.

In the present case, we can choose 5 as the round number.

To determine the length of the line to show 5 km, the following calculations are to be carried out:

• 7.5 km is represented by a line of 15 cm
• 5 km will be represented by a line of 15 × 5/7.5
• or 5 km will be represented by a line of 10 cm

Graphical method:

Hence, option 4 is the correct answer.