Given a social network represented as a graph where the nodes are the users and the edges represent the social relations, and a positive integer k, how to select k nodes to maximize the influence in the network remains an active area of research. In this paper, we consider a variant of the problem in which network users are associated with two parameters: a benefit value and a cost. A fixed budget is given, and the network is partitioned into communities. The task is to select a subset of users (the seed set) within the budget so that their initial activation maximizes the earned profit, while ensuring that each community realizes at least a minimum fraction of its total benefit under a maximin fairness criterion. For any seed set, the earned benefit is defined as the sum of the benefit values of the users influenced by the seed set, and the profit is defined as the difference between the earned benefit and the total cost. Formally, we call this the Fairness-Aware Profit Maximization Problem. We propose a Deep Reinforcement Learning-based approach for solving it: we first model the problem as a Markov Decision Process and subsequently propose a Deep Q-Learning Algorithm. The proposed solution has been implemented and tested on real-world social network datasets. From the reported results, we observed that the proposed approach yields a seed set whose initial activation produces up to 10 times more profit than the baseline methods. The implementation of our methodology is available at https://github.com/PoonamSharma-PY/DRL_FPM.git.