Answer: a) The mobile device is infected with malware
Explanation: When a phone is infected by a malware, one of the effect is quick or fast battery drain or a spike in data usage. This is because the malware performs background activities even when you are not using the phone (e.g sending data which will result in spike of data usage) making it constantly active which will require more battery power; that explains the fast battery drain.
The mobile phone might have gotten the malware from the unsecure public wifi or used the wifi to download an application from an untrusted source.
Since the user is experiencing faster than normal battery drain after using the public wifi, his device is most likely infected with malware.