govt job

Doing regular degree with your full time government job is not advisable as it would cause problems later and could lead to a disciplinary action against you.

You can either take permission from the department you work in and ask for leave to continue studies or you can opt for distance learning or correspondence degree

Yes, it can be pursued with permission of department as per rules. 

If the degree is helpful in your job knowledge, you may seek specific permission from your employer.   If you have filled the application showing your status as an employee, it is mandatory to submit an 'Employer Approval' letter.  Please obtain permission, informing the regular hours of courses and how the knowledge helps your employer, and how the working hours during employment and college working hours do not clash, and assure that taking up the course in no way affects your performing duties.

How you could you travel in boats at the same time?

The basic answer to your query is "No". An individual cannot do Government job and regular Graduation at the same time. But you can do distance graduation with the government jobs. However, in some jobs it can be approved (based upon the positions), if proper approval from the competent authority of the Department in this regard has been obtained.

Hope It Helps

Regards
Kevin M. Paul