Why the lower torque and not the higher?

If the torque obtained from the shear stress limit was substituted into the angle of twist formula, we would compute a shaft twist angle greater than the $1^{\circ }$ limit and this is not an acceptable solution. On the other hand, if we substituted the torque obtained from the angle of twist formula into the shear stress equation, we would find that the shear stress produced in the shaft would be less than the $50 \mathrm{MPa}$ limit. This is an acceptable result since we are only required to make sure that stresses are no higher than $50 \mathrm{MPa}$

The maximum allowable torque for this shaft is therefore:

$$\begin{gathered} \mathrm{T}=886,079.7 \mathrm{N}-\mathrm{mm} \\ =886.0797 \mathrm{N}-\mathrm{m} \\ =886 \mathrm{N}-\mathrm{m} \end{gathered}$$