Adjoint transport theory is most widely used in perturbation theory. A most common problem here is the determination of the reactivity change in a self-multiplying system due to the insertion of an absorber in a small region. There is, however, a class of problems of the source-detector type where adjoint transport theory proves to be a very effective and fast way of obtaining the desired results. In many practical source problems we want to evaluate the reaction rate, say fissions or absorptions, in a material surrounded by a moderator due to a neutron flux incident on the assembly. Here the main advantage of using the adjoint method as opposed to the conventional real-flux shell-source calculations is a significant reduction in computer time. The reactions induced by each group of source neutrons is obtained from one run of an adjoint problem. To obtain the same information from real-flux calculations we need an individual run for every energy group g. Computer time savings ranging by a factor of 5 to 30 are representative. The theory previously reported by one of us (H.A.S.) in the classified literature is derived and subsequently applied to the following problems. a. the fissions induced in a spherical plutonium-detector foil separated by a moderating layer from an incident collimated neutron beam; b. a neutron-dose-rate detector device consisting of a lithium iodide crystal to register absorptions surrounded by a sphere of polyethylene; c. the theoretical evaluation of the neutronic coupling coefficient between two reactors, as one might visualize in a clustered-Rover nuclear-reactor rocket-engine system.