A bstract The ratios of the branching fractions of the decays Λ c + → pπ − π + , Λ c + → pK − K + , and Λ c + → pπ − K + with respect to the Cabibbo-favoured Λ c + → pK − π + decay are measured using proton-proton collision data collected with the LHCb experiment at a 7 TeV centre-of-mass energy and corresponding to an integrated luminosity of 1 . 0 fb −1 : $$ \begin{array}{l}\frac{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{\pi}^{-}{\pi}^{+}\right)}{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{K}^{-}{\pi}^{+}\right)}=\left(7.44\pm 0.08\pm 0.18\right)\%,\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{K}^{-}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{K}^{-}{\pi}^{+}\right)}=\left(1.70\pm 0.03\pm 0.03\right)\%\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{\pi}^{-}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({\varLambda}_c^{+}\to p{K}^{-}{\pi}^{+}\right)}=\left(0.165\pm 0.015\pm 0.005\right)\%,\hfill \end{array} $$ ℬ Λ c + → p π − π + ℬ Λ c + → p K − π + = 7.44 ± 0.08 ± 0.18 % , ℬ Λ c + → p K − K + ℬ Λ c + → p K − π + = 1.70 ± 0.03 ± 0.03 % ℬ Λ c + → p π − K + ℬ Λ c + → p K − π

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