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ソウル is the pronunciation given in the NHK日本語発音アクセント辞典, but both pronunciations are in use; some speakers pronounce it ソール instead. From The Sounds of Japanese (Vance 2008), pages 67-68: Katakana spellings of recent borrowings and foreign proper names with ウ (u) instead of ー (the length mark) do represent /ou/, but these are rare; Souru ソウル 'Seoul' in ...
Today, きゅう is the default (i.e. productive) on-yomi pronunciation of 九 (or 9) for counting most things, and only a small portion of words requires く. Always: hours (o'clock) (9時, 19時), dates (19日, 29日), month name (9月) Preferred or alternative to きゅう: hours (duration) (9時間, 19時間...), years (9年(間), 2009年...), people (9人, 19人...), degree (29度, 39度...), bare ...
They both mean the same of course, and there is plenty of info you can find explaining that ゆく is an older version. In addition, I have found that ゆく tends to be a more informal version of いく. Perhaps ゆく is also easier to pronounce than いく. I don't hold any data, but FWIW, I think ゆく is used more often than いく is conversation.
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