What is True Altruism? - An Early Morning Preponderance

I stood up for an old lady on the tube the other day (I do this if I have the option), when I say "I stood up" for her, I don't mean that I advocated her rights in a dramatic speech that was described in the Independent as a 'Tour de Force... a brutal indictment of the government's neglect of its ageing population...' and I also don't mean that she was attacked by a mob with knives and pea shooters and that I stood in the way and bravely took the bruises and cuts whilst she and her husband made a dramatic escape to the jubilee line. 

Of course I mean that I literally "Stood up" and gave her my seat. And yet this was enough to put a smile on her face for the few minutes afterwards. How nice of me.

Yes. She was smiling for a few minutes, happy in the knowledge that young people (I use the term loosely since I almost had more hair than she did) have not completely lost that sense of good will towards their elders...

Little did she know that behind the pages of my book that I was reading, and stuffed into the armpit of a large man in an Emirates T Shirt, a smug happiness had begun in my head that would last not just a tube ride, but the WHOLE DAY!

I felt BRILLIANT. It was great to do something nice for someone else and it made my whole day better. I suspect I got far more out of standing up for that lady than she would have had from the pleasure of sitting down.

But this begs the somewhat cynical question (it's one that I grapple with constantly)...

Have I just done something nice because I wanted another person to be happy? OR have I done something nice in order to make myself feel better?

The problem with this question is that I have not been able to find an answer. I do want other people to be happy and I do want to feel happy myself. So is the good deed doer motivated by a desire to help others or themselves? 

Does true Altruism ever exist? I can convince myself that I am doing this for the right reasons but if it didn't feel good for me, I probably wouldn't do it again... or would I?