A new simple gear train shown in Figure below has an input shaft $(1)$ that requires $14$ kW to rotate at $1,800$ revolutions per minute $($RPM$).$ The teeth of the gears are given as follows: $A=21$ teeth, $B=41$ teeth, $C=20,D=37$ teeth, $E=18$ teeth and $F=33$ teeth.

Calculate the speed ratio between shafts $1$ and $2.$ What is the angular speed and torque of shaft $2?$

Calculate the speed ratio between shaft $1$ and shaft $3.$ What is the angular speed and torque of shaft $3?$

Calculate the speed ratio between shaft $1$ and shaft $4.$ What is the angular speed and torque of shaft $4?$

Assume the power efficiency of the whole train gear is reduced to $69\mathrm{.}6\%$ due to mechanical causes, to maintain the current output torque, angular speed and output power, calculate the actual input power in this scenario.