On the whole surface of earth the ratio of land and water is 1:2. The land and water in northern hemisphere is ratio 3 : 4. Then what is the ratio of land and water in southern hemisphere.

Options

A. `5:16`
B. `4:11`
C. `5:11`
D. `4:7`

Answer

To solve the problem, we need to find the ratio of land and water in the southern hemisphere given the ratios in the whole earth and the northern hemisphere.

### Step-by-Step Solution:

1. **Understand the Ratios Given:**
- The ratio of land to water on the whole surface of the Earth is 1:2.
- The ratio of land to water in the northern hemisphere is 3:4.

2. **Calculate Total Parts:**
- For the whole Earth, the total parts = 1 (land) + 2 (water) = 3 parts.
- For the northern hemisphere, the total parts = 3 (land) + 4 (water) = 7 parts.

3. **Assume Total Units:**
- Let’s assume the total area of the Earth is represented by 300 units (100 units of land and 200 units of water).
- Therefore, land = 100 units and water = 200 units.

4. **Calculate Units in Each Hemisphere:**
- Since the Earth is divided into two hemispheres (northern and southern), we can assume each hemisphere has 150 units (half of 300 units).

5. **Calculate the Value of One Unit in the Northern Hemisphere:**
- In the northern hemisphere, the total parts are 7, and we have 150 units.
- Value of 1 unit = Total units in North / Total parts = 150 / 7 = 21.43 (approximately).

6. **Calculate Land and Water in the Northern Hemisphere:**
- Land in the northern hemisphere = 3 parts = 3 * 21.43 = 64.29 (approximately).
- Water in the northern hemisphere = 4 parts = 4 * 21.43 = 85.71 (approximately).

7. **Calculate Remaining Land and Water for the Southern Hemisphere:**
- Total land on Earth = 100 units, and total water = 200 units.
- Land in the southern hemisphere = Total land - Land in northern hemisphere = 100 - 64.29 = 35.71 (approximately).
- Water in the southern hemisphere = Total water - Water in northern hemisphere = 200 - 85.71 = 114.29 (approximately).

8. **Find the Ratio of Land to Water in the Southern Hemisphere:**
- The ratio of land to water in the southern hemisphere = Land : Water = 35.71 : 114.29.
- To simplify, divide both parts by 35.71 = 1 : 3.2 (approximately).
- To express this as a whole number ratio, multiply both sides by 5 to eliminate the decimal = 5 : 16.

### Final Answer:
The ratio of land to water in the southern hemisphere is **5:16**.