A $50m$ long propeller solid shaft for a ship has been designed for a low$-$carbon steel that has an allowable shear stress of $90$MPa. To safely carry the design torque with the low$-$carbon steel requires a solid shaft that has an outside diameter of $375mm.$

It has been decided to change the design from a solid shaft to a hollow shaft made of a stronger alloy steel that has an allowable shear stress of $160$MPa. The $375mm$ outside diameter is to be retained in the redesigned hollow propeller shaft.

Determine the maximum allowable inside diameter $($rounded down to the nearest millimeter$)$ that can be used for the redesigned hollow propeller shaft made of alloy steel.