Firstly it is a very good thought as you are thinking of helping the needy people.
But with or as a Civil service servant, you would e indirectly connected with the poor people. You would be more of a government servant and would serve the nation.
But in-case if you take up Sociology and are a Sociology Graduate followed by an MSW ( Masters in Social work), you would be dirctly working with social issues related to education, poverty, nutrition etc.
Another way is by being a Graduate and work in the corporate sector. Corporates are associated with CSR ( Corprorate Social Responsib
Management can definitely be studied without maths. Hope however you do not hate or are afraid of Maths.
You can pursue MBA in Human Resource which is close to Arts / Humanities and psychology.
Reach out to NGO's in your area and offer them being a volunteer and then gradually you can move to full time work there.
There are many NGO's who employ on salary - Few popular ones in Delhi are:
Salaam Baalak Trust www.salaambaalaktrust.com/
Teach For India www.teachforindia.org/
Helpage India www.helpageindia.org/
A degree in social work or psychology or related humanities streams can also help you join them in full time role.
A quick search on Naukri.Com will also give you fair idea on kind of jobs available in NGO domain in Delhi.
[Is NGO Managem