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Novel table-top sources of extreme-ultraviolet light based on high-harmonic generation yield unique insight into the fundamental properties of molecules, nanomaterials or correlated solids, and enable advanced applications in imaging or metrology. Extending high-harmonic generation to high repetition rates portends great experimental benefits, yet efficient extreme-ultraviolet conversion of correspondingly weak driving pulses is challenging. In this article, we demonstrate a highly-efficient source of femtosecond extreme-ultraviolet pulses at 50-kHz repetition rate, utilizing the ultraviolet second-harmonic focused tightly into Kr gas. In this cascaded scheme, a photon flux beyond ≈3 × 10¹³ s^-1 is generated at 22.3 eV, with 5 × 10^-5 conversionmore » efficiency that surpasses similar harmonics directly driven by the fundamental by two orders-of-magnitude. The enhancement arises from both wavelength scaling of the atomic dipole and improved spatio-temporal phase matching, confirmed by simulations. Finally, spectral isolation of a single 72-meV-wide harmonic renders this bright, 50-kHz extreme-ultraviolet source a powerful tool for ultrafast photoemission, nanoscale imaging and other applications.« less