Several types of weighted-automata models and formalisms to specify and verify constraints on accumulated weights have been studied in the past. The lack of monotonicity for weight functions with positive and negative values as well as for ratios of the accumulated values of non-negative weight functions renders many verification problems to be undecidable or computationally hard. Our contribution comprises polynomial-time algorithms for computing ratio and weight quantiles in Markov chains, which provide optimal bounds guaranteed almost surely or with positive probability on, e.g., cost-utility ratios or the energy conversion efficiency.