Question

Given scale on a map is 1 cm = 20m then its Representative Factor (RF) is

• A. 1 : 1000
• B. 1 : 1500
• C. 1 : 2000
• D. 1 : 2500

Hint:

A quick shortcut to convert a scale of the form "1 cm = X meters" to an RF is:
RF = 1 : (X \( \times \) 100).
In this case, X = 20, so the RF is 1 : (20 \( \times \) 100) = 1 : 2000.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to convert a given engineering scale (1 cm = 20 m) into a Representative Fraction (RF).

Step 2: Key Formula or Approach:
The Representative Fraction (RF) is a dimensionless ratio of the map distance to the corresponding ground distance.
\[ RF = \frac{\text{Map Distance}}{\text{Ground Distance}} \] To calculate RF, both distances must be expressed in the same units.

Step 3: Detailed Explanation:
The given scale is:
\[ 1 \, \text{cm (Map)} = 20 \, \text{m (Ground)} \] We need to convert the ground distance to centimeters.
We know that 1 m = 100 cm.
\[ 20 \, \text{m} = 20 \times 100 \, \text{cm} = 2000 \, \text{cm} \] So, the scale is:
\[ 1 \, \text{cm (Map)} = 2000 \, \text{cm (Ground)} \] Now, we can write the RF:
\[ RF = \frac{1 \, \text{cm}}{2000 \, \text{cm}} = \frac{1}{2000} \] This ratio is expressed as 1 : 2000.

Step 4: Final Answer:
The Representative Factor (RF) is 1 : 2000.
This corresponds to option (C).