If the statement of scale is 3 inch = 1 mile, the Representative Fraction (R. F.) will be :

Question

Accepted Answer

The correct answer is Option 3: 1 : 21,120. Here's why:

**Explanation:**

The Representative Fraction (RF) is a ratio that expresses the relationship between a distance on a map and the corresponding distance on the ground. It's a unitless ratio, meaning both sides of the ratio must be in the same units.

Given the scale 3 inches = 1 mile, we need to convert both sides to the same unit, preferably inches.

*   **1 mile = 5280 feet**
*   **1 foot = 12 inches**
*   Therefore, **1 mile = 5280 feet * 12 inches/foot = 63,360 inches**

So, the scale 3 inches = 1 mile is equivalent to 3 inches = 63,360 inches.

To find the RF, we need to express this as a ratio with '1' on the map side. We divide both sides by 3:

*   (3 inches / 3) = (63,360 inches / 3)
*   1 inch = 21,120 inches

Therefore, the Representative Fraction (RF) is **1 : 21,120**.

**Why other options are incorrect:**

*   **Option 1: 1 : 63,360:** This represents the number of inches in a mile, but it doesn't account for the fact that 3 inches on the map represent that mile. It skips the crucial step of dividing by 3 to get the '1' on the map side of the ratio.

*   **Option 2: 1 : 1,90,080:** This value is obtained by multiplying 63,360 by 3, which is the opposite of what we need to do. We need to divide the ground distance by the map distance to get the RF.

*   **Option 4: 1 : 31,680:** This value is half of 63,360. There's no logical basis for dividing the number of inches in a mile by 2 in this context. It doesn't relate to the given scale of 3 inches = 1 mile.