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Tuesday, June 16, 2015

UPSC Maths Problems Challenge : A Problem A Day! (Day 4)

Today's problem is from Ratio And Proportions.It can be solved in a very easy way by converting the ratios into percentages.Can you solve it in a totally different way?



Today's Problem(16/06/2015)


Question Credit : http://www.m4maths.com

The ratio of land and water on the globe is 1:2 but in the northern hemisphere it is 2:3 The ratio in the southern hemisphere is 

a)4:11    b)3:2     c)4:3     d)2:11

Let the total amount of land be x units and that of water be 2x units.Then,the total area is 
(2x + x) units = 3x units,out of which 1.5x units lies in the northern hemisphere and the other 1.5x units lies in the southern hemisphere.
Therefore, the amount of land present in the northern hemisphere is {(2/5) * 1.5x} units = 0.6x units and the amount of water present in the northern hemisphere is {(3/5) * 1.5x} units = 0.9x units.
So,the amount of land present in the southern hemisphere is (1x - 0.6x) units = 0.4x units and the amount of water present in the southern hemisphere is (2x - 0.9x) units = 1.1x units.
Therefore,the ratio of land and water present in the southern hemisphere is 0.4x/0.11x 
= 0.4/0.11= 4/11 = 4 : 11.

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