A distance of `1//2` cm on a map represents 200 km on the ground. If two cities are 1800 km apart on the ground, then their distance on the map will be

Options

A. 6 cm
B. 9 cm
C. 3 and `1//2` cm
D. 4 and `1//2` cm

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the scale of the map
We know that a distance of \( \frac{1}{2} \) cm on the map represents 200 km on the ground.

### Step 2: Find the scale factor
To find out how many centimeters represent 1 km, we can set up a ratio:
\[ \text{Scale} = \frac{\frac{1}{2} \text{ cm}}{200 \text{ km}} = \frac{1 \text{ cm}}{400 \text{ km}} \]
This means that 1 cm on the map represents 400 km on the ground.

### Step 3: Calculate the distance on the map for 1800 km
Now we need to find out how many centimeters represent 1800 km on the map. We can use the scale we found:
\[ \text{Distance on map} = \frac{1800 \text{ km}}{400 \text{ km/cm}} \]
Calculating this gives:
\[ \text{Distance on map} = \frac{1800}{400} = 4.5 \text{ cm} \]

### Step 4: Convert to a mixed number (if necessary)
4.5 cm can also be expressed as:
\[ 4.5 \text{ cm} = 4 \frac{1}{2} \text{ cm} \]

### Final Answer
The distance between the two cities on the map will be \( 4 \frac{1}{2} \) cm.

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