The easiest way to figure it out is based on the energy conservation laws.
Power out + loss = Power in
If we disregard the losses, Pi = Po
P= Torque *rpm
Since ratio 10 to 1 means RPMout = (RPMin)/10
Pi = 10 (N*m) * RPMin
Po = Tout (N*m) * RPMout = Tout*(RPMin) / 10
or
Tout*(RPMin / 10) = 10*RPMin
Tout = (10*RPMin)/(RPMin/10) = 10*10 = 100 (N*m)