The density of population in a state is 518 persons per sq mile. Define it in per square kilometre, if 1 sq mile = 2.59 sq km.

Options

A. 300 persons per sq km
B. 312 persons per sq km
C. 313 persons per sq km
D. 200 persons per sq km

Answer

To convert the population density from persons per square mile to persons per square kilometer, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data**:
- Population density = 518 persons per square mile
- Conversion factor = 1 square mile = 2.59 square kilometers

2. **Set up the conversion**:
We need to find the density in persons per square kilometer. Since we know that 1 square mile is equivalent to 2.59 square kilometers, we can express the population density in terms of square kilometers.

3. **Calculate the density in persons per square kilometer**:
\[ \text{Density in persons per square kilometer} = \frac{\text{Density in persons per square mile}}{\text{Conversion factor (in square kilometers)}} \]
Substituting the values we have:
\[ \text{Density in persons per square kilometer} = \frac{518 \text{ persons}}{2.59 \text{ sq km}} \]

4. **Perform the division**:
\[ \text{Density in persons per square kilometer} = 518 \div 2.59 \approx 200.77 \text{ persons per sq km} \]

5. **Round the result**:
Since we are dealing with population density, we can round this to the nearest whole number:
\[ \text{Density in persons per square kilometer} \approx 201 \text{ persons per sq km} \]

### Final Answer:
The density of population in the state is approximately **201 persons per square kilometer**.