Battery staus randomly change with 5.0.2 topic

Hi to everyone, i bought from internet second-hand Nexus 4 with 5.0.2 but after a couple of day i got a very strange problem:
The battery % randomly change.
I mean, i am normally (but it happen also in standby) using my N4 when it alert to me that the battery is out.
It pass from 40% (or whatever good %) to 4,5 sometimes 1 and then shut down.
Also, i noticed that sometime i can't find "battery" icon in the option menu.
So i try to rebooth the phone but the touchscreen doesn't work and i need to tap with 2,3 or 4 finger.
When i reboot again, it work but they % keep changing, sometime in a bigger number, sometime in a lower number.

I complete wipe and format my N4 and for 2 days works in the best way, the battery keep the load and so on
but then, here we are again.

I got a couple of screenshot of the battery icon missing in the option, of the % changing but it is very hard make a video of this becouse it happen randomly.

Android is 5.0.2 stock, no root, no bootloader

Ofc the guy that sell to me said the phone was perfect, no problem and all the stuff works good.

it the first time it happen to me..

Please help me if you can becouse i really don't know how to behave.

Many many many thanks, Federico.

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