High quality datasets for question answering exist in a few languages, but far from all. Producing such datasets for new languages requires extensive manual labour. In this work we look at different methods for using existing datasets to train question-answering models in languages lacking such datasets. We show that machine translation followed by cross-lingual projection is a viable way to create a full question-answering dataset in a new language. We introduce new methods both for bitext alignment, using optimal transport, and for direct cross-lingual projection, utilizing multilingual BERT. We show that our methods produce good Swedish question-answering models without any manual work. Finally, we apply our proposed methods on Spanish and evaluate it on the XQuAD and MLQA benchmarks where we achieve new state-of-the-art values of 80.4 F1 and 62.9 Exact Match (EM) points on the Spanish XQuAD corpus and 70.8 F1 and 53.0 EM on the Spanish MLQA corpus, showing that the technique is readily applicable to other languages.