Literally ‘[At] what time and [for] what reason?’ (although Duolingo doesn't accept that yet).
Which hour and which reason?
Interesting and very specific way to ask when and why.
How is "what time and why" not right?
It's accepted now (7 Oct 2015).
But "What time and what reason?" isn't (as of 2/19/2018).
I'm finding these sentences a bit difficult because there is no real context to them. "When is the concert?", and "Why are you happy?" feel like more complete sentences.
I wrote a typo and got it wrong. RIP