Many mobile applications demand selective execution of multiple correlated deep learning inference tasks on resource-constrained platforms. Given a set of deep neural networks, each pre-trained for a single task, it is desired that executing arbitrary combinations of tasks yields minimal computation cost. Pruning each network separately yields suboptimal computation cost due to task relatedness. A promising remedy is to merge the networks into a multitask network to eliminate redundancy across tasks before network pruning. However, pruning a multitask network combined by existing network merging schemes cannot minimise the computation cost of every task combination because they do not consider such a future pruning. To this end, we theoretically identify the conditions such that pruning a multitask network minimises the computation of all task combinations. On this basis, we propose Pruning-Aware Merging (PAM), a heuristic network merging scheme to construct a multitask network that approximates these conditions. The merged network is then ready to be further pruned by existing network pruning methods. Evaluations with different pruning schemes, datasets, and network architectures show that PAM achieves up to 4.87x less computation against the baseline without network merging, and up to 2.01x less computation against the baseline with a state-of-the-art network merging scheme.