My Math Forum what is it in the southern hemisphere?

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 October 9th, 2018, 08:06 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 355 Thanks: 1 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?
 October 10th, 2018, 04:03 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,632 Thanks: 2080 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. Thanks from Ganesh Ujwal
 October 12th, 2018, 06:45 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,414 Thanks: 1024

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