On the whole surface of earth the ratio of land and water is 1:2. The land and water in northern hemisphere is ratio 2 : 3. Then what is the ratio of land and water in southern hemisphere.

Options

A. `4:11`
B. `11:4`
C. `5:12`
D. `4:7`

Answer

To solve the problem step by step, we will analyze the information given and calculate the required ratio of land and water in the southern hemisphere.

### Step-by-Step Solution:

1. **Understanding the Total Ratio of Land and Water on Earth:**
The total ratio of land to water on the whole surface of the Earth is given as 1:2. This means for every 1 part of land, there are 2 parts of water.

Let’s denote the total parts as:
- Land = 1x
- Water = 2x
- Total = 1x + 2x = 3x

For simplicity, we can assume the total surface area of the Earth is 300 units (1x = 100 units and 2x = 200 units).

2. **Dividing the Total into Hemispheres:**
The total surface area of the Earth is divided equally into the northern and southern hemispheres. Therefore, each hemisphere has:
- Total area in each hemisphere = 300 / 2 = 150 units.

3. **Finding the Ratio of Land and Water in the Northern Hemisphere:**
The ratio of land to water in the northern hemisphere is given as 2:3. This means:
- Land = 2y
- Water = 3y
- Total in the northern hemisphere = 2y + 3y = 5y

Since the total area of the northern hemisphere is 150 units, we can set up the equation:
\[ 5y = 150 \]
Solving for y:
\[ y = 150 / 5 = 30 \]

Now we can find the land and water in the northern hemisphere:
- Land in the north = 2y = 2 * 30 = 60 units
- Water in the north = 3y = 3 * 30 = 90 units

4. **Calculating Land and Water in the Southern Hemisphere:**
Since the total land on Earth is 100 units (from step 1) and the total water is 200 units, we can find the land and water in the southern hemisphere by subtracting the values found for the northern hemisphere from the total.

- Land in the south = Total land - Land in the north
\[ \text{Land in the south} = 100 - 60 = 40 \text{ units} \]

- Water in the south = Total water - Water in the north
\[ \text{Water in the south} = 200 - 90 = 110 \text{ units} \]

5. **Finding the Ratio of Land to Water in the Southern Hemisphere:**
Now we can find the ratio of land to water in the southern hemisphere:
\[ \text{Ratio} = \text{Land in the south} : \text{Water in the south} = 40 : 110 \]
To simplify this ratio, we can divide both sides by 10:
\[ \text{Ratio} = 4 : 11 \]

### Final Answer:
The ratio of land to water in the southern hemisphere is **4:11**.