We studied the reversible transitions between two levels of excited molecule stimulated by encounters with other solutes. The inter-system crossing results in either quenching or trapping of excitation depending on the relationship between the lifetimes of the levels. In the particular case of an immobile excited molecule and equal lifetimes, an exact solution of the problem was given which is valid for arbitrary concentration of solutes. We compared the fluorescence quantum yield obtained with this solution, superposition approximation and integral encounter theory. Our main conclusion is that for equal lifetimes the latter has an advantage, even in small concentration limits and is out of competition when the lifetime of the primary excited level is shorter than another.