The scale of a map is `1 : 2 xx 10^(6)`. Two cities are 9 cm apart on the map. The actual distance (in km) between the cities is

Options

A. 180
B. 270
C. 360
D. 135

Answer

To solve the problem, we need to find the actual distance between two cities based on the scale of the map and the distance between the cities as represented on the map.

### Step-by-Step Solution:

1. **Understand the Scale of the Map**:
The scale given is \(1 : 2 \times 10^6\). This means that 1 unit on the map corresponds to \(2 \times 10^6\) units in reality.

2. **Distance on the Map**:
The distance between the two cities on the map is given as 9 cm.

3. **Calculate the Actual Distance**:
To find the actual distance, we can use the scale:
\[ \text{Actual Distance} = \text{Distance on Map} \times \text{Scale Factor} \]
Substituting the values:
\[ \text{Actual Distance} = 9 \, \text{cm} \times (2 \times 10^6) \]
\[ \text{Actual Distance} = 18 \times 10^6 \, \text{cm} \]

4. **Convert Centimeters to Kilometers**:
We need to convert the distance from centimeters to kilometers. We know that:
- 1 kilometer = 1000 meters
- 1 meter = 100 centimeters
Therefore,
\[ 1 \, \text{km} = 1000 \times 100 = 10^5 \, \text{cm} \]
To convert centimeters to kilometers, we divide by \(10^5\):
\[ \text{Actual Distance in km} = \frac{18 \times 10^6 \, \text{cm}}{10^5} \]
\[ \text{Actual Distance in km} = 18 \times 10^{6 - 5} = 18 \times 10^1 = 180 \, \text{km} \]

5. **Final Answer**:
The actual distance between the two cities is **180 km**.