Question

If the ratio of land and water on earth is in the ratio of 1:2 and the ratio of land and water in the northern hemisphere is 2:3, what is the ratio of land and water in the southern hemisphere?

Answer 1

Step 1. Given data:

The ratio of land and water on earth = $1:2$

The northern hemisphere ratio of land and water = $2:3$

Step 2. Calculation:

For the whole earth, land = $\frac{1}{1+2}=\frac{1}{3}$
And water= $\frac{2}{1+2}=\frac{2}{3}$
∴ For the northern hemisphere, land= $\frac{2}{5}\times \frac{1}{2}=\frac{1}{5}$
and water= $\frac{3}{5}\times \frac{1}{2}=\frac{3}{10}$​ ​as northern hemisphere = $\frac{1}{2}$​of the whole earth.
∴ the southern hemisphere, land = $\frac{1}{3}-\frac{1}{5}=\frac{2}{15}$
Water = ​$\frac{2}{3}-\frac{3}{10}=\frac{11}{30}$
∴ The required ratio of land:water in the southern hemisphere = $\frac{2}{15}:\frac{11}{30}=4:11$
Hence, the ratio of land to water in the Southern Hemisphere is $4:11$