Question:easy

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

Show 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.
  • 1 : 1000
  • 1 : 1500
  • 1 : 2000
  • 1 : 2500
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Understand what Representative Fraction is really asking for.
RF is nothing but a pure, unit free ratio that tells you how many real world units correspond to one unit on the map, so before we can write it as a fraction we must express both the map distance and the ground distance in exactly the same unit.
Step 2: Bring both sides of the given scale into centimetres.
We are told 1 cm on the map equals 20 m on the ground. Converting the ground side into centimetres using $1 \text{ m} = 100 \text{ cm}$:
\[ 20 \text{ m} = 20 \times 100 = 2000 \text{ cm} \] So the scale, in matching units, reads 1 cm (map) : 2000 cm (ground).
Step 3: Write it as the Representative Fraction.
Once both sides share the same unit, they simply cancel out and leave a pure number ratio:
\[ RF = 1 : 2000 \] This tells us that any single unit of length on the map represents 2000 of that same unit on the actual ground, regardless of whether we measure in centimetres, inches, or anything else.
\[ \boxed{1 : 2000} \]
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