Resolving the distance and velocity of objects with high accuracy is needed in 3D vision, and light detection and ranging (LiDAR) provides this via the temporally-resolved detection of backscattered short-pulsed light from imaged objects1,2. Simultaneous improvements in the speed and signal-to-noise ratio of photodetectors are needed to enable demanding ranging applications. Silicon, in view of its low cost and ease of monolithic integration, has been a primary option for LiDAR photodetectors in the range of 850 to 950 nm; however its indirect bandgap leads to low absorption coefficient in the NIR3,4 and a trade-off between speed and efficiency. Here we report solution-processed PbSn binary perovskite photodetectors that unite external quantum efficiency of 85% at 850 nm with a dark current below 10-8 A/cm2 and response faster than 100 picoseconds. The combined efficiency×speed is >2x higher than in fast silicon photodetectors and >100x higher than in the best previously-reported solution-processed photodetectors. We develop self-limiting self-reduced Sn precursors that enable perovskite crystallization at the desired stoichiometry and prevent the formation of interfacial defects with the hole transport layer. The approach removes oxygen from the solution, converts Sn4+ to Sn2+ through comproportionation, and leaves neither Sn nor SnOx. We resolve sub-mm distances, highlighting the potential of solution-processed perovskite photodetectors in LiDAR.