Recent progress has been experienced in the field of hypernuclear weak decay, especially concerning the ratio of the neutron-to proton-induced Λ nonmesonic decay rates, Γ n /Γ p . Theoretical analyses of nucleon coincidence data have been performed in a finite nucleus framework. They led to the extraction of Γ n /Γ p values in agreement with pure theoretical estimates, thus providing an evidence for the solution of a longstanding puzzle. Here we present an alternative approach to the problem, based on a nuclear matter formalism extended to finite nuclei via the local density approximation. The work is motivated by the exigence to make the determination of Γ n /Γ p from data less model dependent. One-meson-exchange potentials are used for describing both the oneand two-nucleon induced decays, ΛN → nN and ΛN N → nN N . For the latter, treated within a microscopic approach, the channels Λnn → nnn and Λpp → npp are included in addition to the mode Λnp → nnp already considered, in a phenomenological way, in previous studies. The propagation of the final nucleons in the residual nucleus is simulated by an intranuclear cascade code. We evaluate single and double coincidence nucleon spectra for the nonmesonic decay of 12 Λ C. Through the comparison of our predictions with KEK coincidence data we determine Γ n /Γ p = 0.43 ± 0.10 for this hypernucleus, confirming previous finite nucleus analyses. The use of a high nucleon kinetic energy detection threshold such as 60 MeV makes the contribution of twonucleon induced channels quite small, but final state interaction effects are still important when extracting Γ n /Γ p from measured single nucleon distributions. Coincidence spectra suffer less from these effects even for a moderate detection threshold such as 30 MeV. In any case, final state interactions have to be considered for meaningful determinations of Γ n /Γ p . 21.80.+a, 13.30.Eg, 13.75.Ev