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:
B(Λ+c→pπ−π+)B(Λ+c→pK−π+)=(7.44±0.08±0.18)%,B(Λ+c→pK−K+)B(Λ+c→pK−π+)=(1.70±0.03±0.03)%B(Λ+c→pπ−K+)B(Λ+c→pK−π+)=(0.165±0.015±0.005)%,
where the uncertainties are statistical and systematic, respectively. These results are the most precise measurements of these quantities to date. When multiplied by the world-average value for B(Λ+c→pK−π+), the corresponding branching fractions are
B(Λ+c→pπ−π+)=(4.72±0.05±0.11±0.25)×10−3,B(Λ+c→pK−K+)=(1.08±0.02±0.02±0.06)×10−3,B(Λ+c→pπ−K+)=(1.04±0.09±0.03±0.05)×10−4,
where the final uncertainty is due to B(Λ+c→pK−π+).