A two$-$stage speed$-$reducer gearbox containing a compound reverted gear train transmits $35$ hp with an input speed of $1200$ rpm $.$ Spur gears with $20$ pressure angle are used, with $16$ teeth on each of the small gears and $48$ teeth on each of the larger gears. A diametral pitch of $10$ tooth$/$in is proposed. Determine the following:

$($a$)$ Train value, $e=$

$($b$)$ Output shaft speed, $n_{\text{o}\text{u}\text{t}\text{p}\text{u}\text{t}}=q,$

$($c$)$ Input torque, $T_{\text{i}\text{n}\text{p}\text{u}\text{t}}==.$

$($d$)$ Output torque, $T_{\text{o}\text{u}\text{t}\text{p}\text{u}\text{t}}=$