Alarming Infection rate reported on AVAST installed Win8 PCs

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Good afternoon all
Finally I get my hands on my daughters laptops (the are back from school for the hols) and was logging on as the Admin account (they have USER accounts and separate account if elevated priv needed) and I get a an AV alert.

OK, all stop.
Check the Win updates are good, they are
Check AVAST is up to date, it is Program version 2014.09.0.2021 and def ver is 140727-0
Start a boot scan with option to DELETE when a virus/problem is found.
OK I can understand the few PUP or ADW alerts but when I see Trj being reported I start to wonder HOW?

The girls say they have not done anything untoward and I am inclined to believe them, they just expect that 'AVAST will protect' .

I've explained about defence in depth but I think it is going on deaf teenage ears.....

My question is this.
Is there some other actions I should be doing with AVAST or other steps they could take?
Currently, as a second scan/run through, I have using the Sophos Virus Removal Tool to run a once only scan; only because it is my work corporate solution.

Your help and pointers appreciated.
Fletch

[Secondmineboy]

If you want a checkup follow this guide and attach the logs here(Use the attachments and other options function under
the answer box: https://forum.avast.com/index.php?topic=53253.0

avast! 2014: Scheduling a Boot-time scan  http://www.avast.com/en-eu/faq.php?article=AVKB132#artTitle

Important:
Please be advised, that the Boot-time scan is an advanced and purposeful feature designed to be used only when there’s something bad going on the system, and usually takes some time before it finishes. That's why it cannot be scheduled to run every time the computer starts, but as needed only.

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I have a few suggestions:

1.  Instead of having your settings as "Delete" when a virus is found, change it to put in "Virus Chest."  You may accidentally get rid of a vital system file by deleting it.  When it is in the Chest, it is safe and away from other parts of the machine, and can later be scanned again to make sure it is real malware vs. a false positive.

2.  Did you install Sophos while you had Avast installed or did you uninstall Avast using the Avast Uninstaller Tool while using Sophos?  The reason I ask is because you can't run 2 AV's at the same time because it creates havoc and can create false postitives.

3.  Do you have MBAM (Malwarebytes) on your machine?  If not, I recommend it (esp. the Premium version - resident).  It compliments Avast yet works differently and layers your security protection.

Otherwise, follow the instructions for attaching your logs in the previous post so a malware removal specialist can review them.  Let us know if you have any questions.  Thank you.