On a map 1 cm represents 1250 km on ground. For 500 km on ground, what is the distance on map?

Options

A. 0.5 cm
B. 4 mm
C. 2.5 mm
D. 12.5 mm

Answer

To solve the problem of finding the distance on a map that represents 500 km on the ground, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scale**: We know that on the map, 1 cm represents 1250 km on the ground.

2. **Set Up the Proportion**: We need to find out how many centimeters on the map correspond to 500 km on the ground. We can set up a proportion based on the scale:
\[ 1 \text{ cm} \text{ (map)} = 1250 \text{ km} \text{ (ground)} \]

3. **Calculate the Distance on the Map**: To find out how many centimeters correspond to 500 km, we can use the unitary method:
\[ \text{Distance on map} = \frac{500 \text{ km}}{1250 \text{ km/cm}} \]
This simplifies to:
\[ \text{Distance on map} = \frac{500}{1250} \text{ cm} \]

4. **Simplify the Fraction**: We can simplify \(\frac{500}{1250}\):
\[ \frac{500}{1250} = \frac{500 \div 250}{1250 \div 250} = \frac{2}{5} \text{ cm} \]

5. **Convert to Decimal**: Now, we can convert \(\frac{2}{5}\) cm to a decimal:
\[ \frac{2}{5} = 0.4 \text{ cm} \]

6. **Convert to Millimeters**: Since 1 cm = 10 mm, we can convert 0.4 cm to millimeters:
\[ 0.4 \text{ cm} = 0.4 \times 10 \text{ mm} = 4 \text{ mm} \]

### Final Answer:
The distance on the map that represents 500 km on the ground is **4 mm**.