Measurements of $b$-hadron lifetimes are reported using $pp$ collision data, corresponding to an integrated luminosity of 1.0fb$^{-1}$, collected by the LHCb detector at a centre-of-mass energy of $7$Tev. Using the exclusive decays $B^+to J/psi K^+$, $B^0to J/psi K^*(892)^0$, $B^0to J/psi K^0_{rm S}$, $Lambda_b^0to J/psi Lambda$ and $B^0_sto J/psi phi$ the average decay times in these modes are measured to be $tau_{B^+to J/psi K^+}$ = $1.637 pm$ 0.004 $pm$ 0.003 ps, $tau_{B^0to J/psi K^*(892)^0}$ = $1.524 pm$ 0.006 $pm$ 0.004 ps, $tau_{B^0to J/psi K^0_{rm S}}$ = $1.499 pm$ 0.013 $pm$ 0.005 ps, $tau_{Lambda_b^0to J/psi Lambda}$ = $1.415 pm$ 0.027 $pm$ 0.006 ps and $tau_{B^0_sto J/psi phi}$ = $1.480 pm$ 0.011 $pm$ 0.005 ps, where the first uncertainty is statistical and the second is systematic. These represent the most precise lifetime measurements in these decay modes. In addition, ratios of these lifetimes, and the ratio of the decay-width difference, $DeltaGamma_d$, to the average width, $Gamma_d$, in the $B^0$ system, $Delta Gamma_d/Gamma_d = -0.044 pm 0.025 pm 0.011$, are reported. All quantities are found to be consistent with Standard Model expectations.
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