Dualising consistent IIA/IIB truncations

We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on S3 and Hp,q and work out the explicit reduction formulas in the internal sector. We also present uplifts for other gaugings of 7-d maximal SUGRA, including theories with a trombone gauging. Some of the latter can only be obtained by a non-geometric compactification.