Question

The ratio of land to water on the whole of earth is 1:2 and 2:3 in the northern hemisphere. Find outthe ratio of water to land in the southern hemisphere

Answer 1

The basic key to the question is that Earth has two hemispheres which are equal. If we figure out this logic we can easily solve this question. Since the ratio of land to water on earth is 1:2 let us assume the proportion to be 1x and 2x , therefore the total volume would be 3x. Since each of these two hemispheres share these resources equally, the share of northern hemisphere is (3/2)x.

It is also given that the ratio of Land to water in N.H is 2:3, using ratios and proportions we can find the volume of land and Water separately.

Volume of land in N.H = (3/2)x X (2/5) = 3x/5

Volume of water in N.H = (3/2)x X (3/5) = 9x/10

Since we know the total volume of land and water present on earth is 1x and 2x respectively. we can deduce the following.

Volume of land in S.H = 1x-3x/5 = 2x/5

Volume of water in S.H = 2x-9x/10 = 11x/10

Finding the ratio of land to water in S.H :  2x/5 : 11x/10 which is 4:11.

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Answer 2

Answer:

$\frac{4}{11}$

Step-by-step explanation:

Given,

The ratio of land to water in earth = 1 : 2

Let land in earth = x and water = 2x

Total = x + 2x = 3x

Where, x is any number,

Now, in each hemisphere is $\frac{1}{2}$ of the earth area,

Thus, the total area of northern hemisphere = $\frac{3x}{2}$

The ratio of land to water in the northern hemisphere is 2 : 3,

Let land in northern hemisphere =2y and water = 3y,

Where, y is any number,

⇒ $2y + 3y = \frac{3x}{2}$

$5y = \frac{3x}{2}$

$y=\frac{3x}{10}$

So, land in northern hemisphere = $\frac{3x}{5}$ and water = $\frac{9x}{10}$,

∵ The ratio of land and water in southern hemisphere

$=\frac{\text{Land of earth - land of northern hemisphere}}{\text{Water of earth - water of northern hemisphere}}$

$=\frac{x-\frac{3x}{5}}{2x-\frac{9x}{10}}$

$=\frac{\frac{5x-3x}{5}}{\frac{20x-9x}{10}}$

$=\frac{\frac{2x}{5}}{\frac{11x}{10}}$

$=\frac{20}{55}$

$=\frac{4}{11}$