Isn't the real issue that his battery discharged from 100% to 47% but the percentages in the battery stats don't come anywhere close to accounting for that drain?
I have this issue occasionally on my Nexus 5 (not X) on stock MM. I can go a week sometimes with all the percentages adding up to the total (very reasonable) battery drain and then BAM.... I'll jump from 0.4%/hour standby to 4-5%/hour with no accompanying increase in the individual percentages. Rebooting always cures it temporarily.
It seems to be triggered by transitions from WiFi to cell data and them back. But not always. I am near certain that it is not a rogue app since I only have a few very ordinary and mature apps installed. I've been trying to get Google's attention, but they seem to be ignoring the issue.
Note that I loaded KK 4.4.4 a while back and it did the same thing, as did my Moto X (2013) on 4.4.4 and 5.1 before I switched to the Nexus 5.
Paul