What is the Representative Fraction (R.F.) if the statement scale is 2 cm = 1 km ?

Question

Accepted Answer

The Representative Fraction (R.F.) is a ratio that expresses the relationship between a distance on a map and the corresponding distance on the ground. It's expressed as 1:X, where 1 unit on the map represents X units on the ground.

To determine the R.F. for the statement scale 2 cm = 1 km, we need to convert both measurements to the same unit. Let's convert kilometers to centimeters:

1 km = 1000 meters
1 meter = 100 centimeters
Therefore, 1 km = 1000 * 100 = 100,000 cm

So, the statement scale 2 cm = 1 km is equivalent to 2 cm = 100,000 cm.

To express this as a Representative Fraction (1:X), we need to make the map distance equal to 1. We can do this by dividing both sides of the equation by 2:

(2 cm / 2) = (100,000 cm / 2)
1 cm = 50,000 cm

Therefore, the Representative Fraction is 1:50,000. This confirms that **Option 3 is correct.**

Now, let's explain why the other options are incorrect:

*   **Option 1: 1 : 1,00,000:** This would imply that 1 cm on the map represents 100,000 cm (or 1 km) on the ground. However, the given scale is 2 cm = 1 km. Therefore, this option is incorrect because it doesn't account for the 2 cm on the map representing 1 km on the ground.

*   **Option 2: 1 : 2,00,000:** This would imply that 1 cm on the map represents 200,000 cm (or 2 km) on the ground. This is incorrect because the given scale is 2 cm = 1 km, not 2 cm = 2 km.

*   **Option 4: 1 : 10,000:** This would imply that 1 cm on the map represents 10,000 cm (or 0.1 km) on the ground. This is incorrect because the given scale is 2 cm = 1 km, which is a much larger ground distance represented by the map distance.

In conclusion, only Option 3 (1 : 50,000) accurately represents the relationship between the map distance and the ground distance as defined by the statement scale 2 cm = 1 km.