I'll be the first to admit that I am very spoiled when it comes to my k-dramas. I'm a fan of clean shots, sharp and bright cinematography and plot development.
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Chart Running Scholar had the basics to pull me in - time slip/ joseon mixed in with modern day. Of course if you want to throw fate in and a dash of romance I'm happy about that too. And they did, and that's why I bothered to watch all 6 episodes (and I say all 6 -- but each one is around 15 minutes give or take so really, there's no excuse not to watch it!). There are enough short, sweet moments that make it worth the watch. If this had been planned out for a few more episodes with a little more detail about things I'd have liked it more. The cast is fine and noone seemed out of their depth. .. So, as it is for a bit of something to watch on a lazy Monday night it's ok.
The best line out of the whole 6 eps was this: "I got excited because I thought you were mad hot!" LOL
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The things that bothered me / made it somewhat less enjoyable (and hence my ratings) were things like it felt like it was shot with someone's iPhone (without a good editing/color/ brightness adjustment). *I did mention I'm spoiled about things like that*. I expect that this was someone's project done on a shoestring budget and if that's the case I'd knock the rating up another notch because well, budget. Some of it could have been edited better for clarity and to move the plot along.

Overall, I'd suggest giving it a watch. Really!