I am the single programmer working on a website handling both frontend and backend. Recently in my task list I have to provide a social news feed (activities among friends) which should summarize activities from different modules (at least 7 modules). It has taken at least 20-25 days for me to develop that. Remember in news feed every action can be performed right on the news feed + there must be some kind of aggregation which should aggregate similar activities e.g. User A, B and C liked your item.
How can I convince my client that the task was complex and the time I took is fair?