It does seem like a riddle
Here's my answer (if I understand the OP properly) ..
Your bank has in it - $1780
1) You brought 20 btc @ $89 for a total of $1780
Your bank now has - $0
2) You cash out 10 btc @ $116 for a total of $1160
Your bank now has - $1160
You have a 'loss' of $620
You have made $0 profit, according to your statements you have made a loss
(you could've brought wow gold and sold some back for all anyone knows)
3) You pay $0 tax.
Your net started off at - $1780
Your net at the end of accounting is - $1160 (and 10 btc, which are not recognized, you can try stating it..)
$620 would be expenditure/loss
(exchange rates don't come into it from this PoV)
That's how I'd write it up in the UK anyway