Alternator or Battery?! Short circuited... :(

[YoungDan]

Brief history to how this happened...

My stupid radio comes on itself in the middle of the night.
So
I set my volume to the lowest when I lock up at night incase it comes on, it must of come on and I didnt use the car for a few days.
Battery died.
Asked my mum to user her car to jump start my car, yeah thats fine.
So i hook up the jump leads to mine, while she does them to hers.
Bad times.
She puts them on the wrong way round and short circuits my car.
Jump started it properly and it just cut out when i removed the leads.
Replaced the battery and everything seemed good...
For 20 minutes into my journey and the battery just goes.
Im assuming its the alternator gone?!
Shall I just replace it, or is there anything else to check before I do?!

Also, is the alternator a hard job? Been offered a second hand one off a 2008 GTi for £50.

Thanks in advance. :)

[snapey]

Get a meter across the battery if you can when the engines running.

If your getting 14v it's not the alternator but 12v or less it's not being charged which means it's the alternator unless there's a short to deck between that and the battery which would be highly doubtful.

As for used I'd be very unsure about buying it because it could just end up being a dud or pack up in 6 months and you've got no guarantee, give VW a ring in the morning to find out how much a new one is but I'd guess the underside of 200.

If any sections don't make sense or are slept incorrect I blam it all on the iPhone 

hope this helps, luke