Reasoning models have gained significant attention due to their strong performance, particularly when enhanced with retrieval augmentation. However, these models often incur high computational costs, as both retrieval and reasoning tokens contribute substantially to the overall resource usage. In this work, we make the following contributions: (1) we propose a retrieval-augmented reasoning model that dynamically adjusts the length of the retrieved document list based on the query and retrieval results; (2) we develop a cost-aware advantage function for training of efficient retrieval-augmented reasoning models through reinforcement learning; and (3) we explore both memory- and latency-bound implementations of the proposed cost-aware framework for both proximal and group relative policy optimization algorithms. We evaluate our approach on seven public question answering datasets and demonstrate significant efficiency gains, without compromising effectiveness. In fact, we observed that the model latency decreases by ~16-20% across datasets, while its effectiveness increases by ~5% on average, in terms of exact match.