The correct option is B friends are going
The given email is written in order to seek permission "to go on an
excursion". This excursion is yet to happen, for which the person
'Ritik' is asking for permission to attend.
Option C: 'Friends are going' is in the present continuous tense. This tense indicates that an action is going on, but may not be going on at the time of speaking.
It means here that Ritik's friends are planning to go.
This is the most suitable option, hence C is correct.
Option A: 'Friends have gone' is in the present perfect tense. It indicates that an action has just been completed in the present. But here, the action is yet to happen. Hence option A is incorrect.
Option B: 'Friends were going' is in the past continuous tense. It indicates an action that was going on at a particular time in the past. But the action here refers to the future. Hence B is incorrect.
Option D: Similarly, 'friends went' is in the simple past tense. It indicates an action that happened in the past. Hence D is also incorrect.