Understanding images and text together is an important aspect of cognition and building advanced Artificial Intelligence (AI) systems. As a community, we have achieved good benchmarks over language and vision domains separately, however joint reasoning is still a challenge for state-of-the-art computer vision and natural language processing (NLP) systems. We propose a novel task to derive joint inference about a given image-text modality and compile the Visuo-Linguistic Question Answering (VLQA) challenge corpus in a question answering setting. Each dataset item consists of an image and a reading passage, where questions are designed to combine both visual and textual information i.e., ignoring either modality would make the question unanswerable. We first explore the best existing vision-language architectures to solve VLQA subsets and show that they are unable to reason well. We then develop a modular method with slightly better baseline performance, but it is still far behind human performance. We believe that VLQA will be a good benchmark for reasoning over a visuo-linguistic context. The dataset, code and leaderboard is available at https://shailaja183.github.io/vlqa/.