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October 9th, 2018, 09:06 PM   #1
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what is it in the southern hemisphere?

The ratio of land and water on our planet is 1 : 2. If this ratio 2 : 3 in the northern hemisphere, what is it in the southern hemisphere?

I following this method:
In a planet, there are two parts: Northern hemisphere and southern hemisphere.
Let total area of planet is 60. (Why we assume 60? Because ratios given, 1+2 = 3 and 2+3 = 5, it should be multiple of this to make calculation easy.)
Ratio of land and water on planet = 1:2
So land on planet = (1/3)×60 = 20
Water on planet = (2/3)× 60 = 40
Area of northern hemisphere = area of southern hemisphere = 30
Given, ratio of land and water on north hemi. = 2 : 3
So, land on north.hemi = (2/5)×30 = 12
water on north. Hemi = (3/5)×30 = 18
Ramaining land and water of planet will be on southern hemi.
land on south hemi = land on planet – land on north hemi
= 20- 12 = 8
water on south hemi = water on planet – water on north hemi
= 40 – 18 = 22
Hence ratio is 8:22 i.e. 4:11

Is there any simple solution to solve this one?
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October 10th, 2018, 05:03 AM   #2
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Using 60 for total area (30 per hemisphere), i.e. land area = 20 and water area = 40,
northern hemisphere has land area = 30×2/(2+3) = 12 and water area = 30 - 12 = 18.
Hence southern hemisphere has land area = 20 - 12 = 8 and water area = 40 - 18 = 22,
and so the land:water ratio for the southern hemisphere is 8:22, which is 4:11.

The above is essentially the same as what you did, but given more compactly.
I can't find a simpler method.

With further compaction, 2 + 1 = 3 and 2(3 + 2) = 10,
so rewriting 1:2 as 10:20 and 2:3 as 6:9, the required answer is (10 - 6):(20 - 9), i.e. 4:11.

That's effectively the same method, but it's less clear why it works when it's written so compactly.
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October 12th, 2018, 07:45 PM   #3
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https://www.algebra.com/algebra/home...on.885553.html
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