A $230$ V d$.$c$.$series motor operates at a rated speed of $900$ r$.$p$.$m$.$ and rated current of $85$ A$.$ The armature circuit resistance is $0\mathrm{.}15$ and the series field resistance is $0\mathrm{.}2.$ Due to saturation effects, the flux at an armature current of $30$ A is $40\%$ of that at an armature current of $85$ A$.$ Calculate $($a$)$ the power rating of the machine in hp; $($b$)$ the motor speed in r$.$p$.$m$.$ when the armature voltage is $230$ Vand the armature current is $30$ A; $($c$)$ the output torque in$($b$)$ if the machine is operating at $85\%$ efficiency