Question

On the entire Earth the ratio between land and water is 1:2 and in the Northern Hemisphere the ratio is 2:3 what will be the ratio of land with water in the Southern Hemisphere ?
A.11:4
B.4:11
C.15:4
D.4:15

Answer 1

Find the total land and water on Earth using the help of ratio of total land with water on Earth . Similarly find the total land and water in the Northern Hemisphere using the help of ratio of total land with water in the Northern Hemisphere and subtract them to find the land and water in the Southern Hemisphere . Divide to find the ratio .

Complete step-by-step answer:
Ratio of land to water on Earth = $\dfrac{1}{2}$
Ratio of land to water on the Northern Hemisphere = $\dfrac{2}{3}$
Let the total area on Earth be A .
We know that the hemispheres divide the Earth into two equal parts .
therefore the area in Northern Hemisphere and area in Southern Hemisphere is $\dfrac{A}{2}$
now total land on Earth = $A \times \dfrac{1}{{1 + 2}} = \dfrac{A}{3}$
and total water on Earth = $A \times \dfrac{2}{{1 + 2}} = \dfrac{{2A}}{3}$
In Northern Hemisphere $\left( {\dfrac{A}{2}} \right)$ $ \to $
Total land = $\dfrac{A}{2} \times \dfrac{2}{{2 + 3}} = \dfrac{A}{5}$
Total water = $\dfrac{A}{2} \times \dfrac{3}{{2 + 3}} = \dfrac{{3A}}{{10}}$
Thus the land in Southern Hemisphere = land on Earth – land in Northern Hemisphere
$ \Rightarrow $ Total land in Southern Hemisphere = $\dfrac{A}{3} - \dfrac{A}{5} = \dfrac{{5A - 3A}}{{15}} = \dfrac{{2A}}{{15}}$
Similarly ,
Water in Southern Hemisphere = water on Earth – water in Northern Hemisphere
$\dfrac{{2A}}{3} - \dfrac{{3A}}{{10}} = \dfrac{{20A - 9A}}{{30}} = \dfrac{{11A}}{{30}}$
Therefore ratio of land and water in Southern Hemisphere = $\dfrac{{\dfrac{{2A}}{{15}}}}{{\dfrac{{11A}}{{30}}}} = \dfrac{4}{{11}} = 4:11$ ( on dividing the above two quantities )
Note – In these types of questions it is required to know the concept behind finding ratio using the given information . Calculation of ratios and the conversion of ratios into areas using variables should be understood properly .