Based on maximum shearing stress, τmax = 16T / πd3:
Steel
$\tau_{st} = \dfrac{16(3T)}{\pi(50^3)} = 83$
$T = 679\,042.16 \, \text{N}\cdot\text{mm}$
$T = 679.04 \, \text{N}\cdot\text{m}$
Aluminum
$\tau_{al} = \dfrac{16T}{\pi (40^3)} = 55$
$T = 691\,150.38 \, \text{N}\cdot\text{mm}$
$T = 691.15 \, \text{N}\cdot\text{m}$
Based on maximum angle of twist, θmax = 6°:
$\theta = \left( \dfrac{TL}{JG} \right)_{st} + \left( \dfrac{TL}{JG} \right)_{al}$
$6^\circ \left( \dfrac{\pi}{180^\circ} \right) = \dfrac{3T(900)}{\frac{1}{32}\pi (50^4)(83\,000)} + \dfrac{T(600)}{\frac{1}{32}\pi (40^4)(28\,000)}$
$T = 757\,316.32 \, \text{N}\cdot\text{mm}$
$T = 757.32 \, \text{N}\cdot\text{m}$
Use the least value of T. Thus, T = 679.04 N·m answer