I think it's because of the following, but correct me if I'm wrong: The г is there because the ending -ого is added because the word is in genitive case here. Whenever you have a genitive case ending the г is pronounced as a 'v'. The same goes for example моего (which means mine) in which case -его is the genitive ending.
That's just the way it is :p. English itself is also not very consistent in its pronunciation, take e.g. the words 'heart' , 'beard' and 'heard' which all have different vowel sounds.
I think the 'v' in '-ого' and '-его' is maybe a bit softer than the 'в' but I'm not really sure.
As a native Russian speaker I would assume that the spoken "v" from written "g" is easier to speak if you now what I mean. Try e.g. To speak (in English) gogogogo(4x go) fast and then vovovovo(4x vo) fast, you'll eventually see that the latter is faster or easier to speak fast
@ MaaxiMcDonat Thank you for demonstrating the fluidity of sounds and how letters are at best relative :)
It depends. For example, when u use it in Kogda (when) it sounds same as G. But somtimes it can be pronunaced different. Like V. Skoroga (skorava), Kogo (kavo) etc. Can you see the difference? in "kogdo" after the G next is D but in "skorogo" or in "kogo" after the G the next one is O, I mean a vowel. Another example is Ego (his) sounds like "Yevo".
Oh, I didn't know that one-syllable particles can be stressed or not stressed depending on the surrounding words. http://www.russianstress.info/index.php/main/view/stress
The Duolingo pronunciation of скорого sounds like "skorovuh" but when looking at Forvo - a website I rely on when learning how to pronounce anything - some of the example speakers pronounce the г as a "v" while others say "w" and some are a mix in between. This leads me to think that the genitive ending -ого does something similar to English when words like "dough" or "sign" have a silent "g" sound. Hearing some native speakers say скорого with a "w" sound is odd since the sounds don't exist in the Russian language but I suppose it could be called a soft "v" since some people do say it with a distinct "v" sound as well. It makes sense to me that when translating words with a "w" into Russian, it's replaced with в if the "w" sound can be considered a soft "v".
Formal would be "До свидания", which is universal, or "До скорого свидания" — if you know that you definitely will see the listener(s) pretty soon. For example, you can use "До скорого свидания" if today you have a meeting with your classmate/colleague, and tomorrow you will see each other at school/college/work. Or today is Friday and you will see them on Monday.