Bob..thank you very much for taking time with my question but I still don't seem to get it. the book answers are

a=672 N.m
b=14.1 KW

to re-iterate the problem...a shaft rotating @ 800 rpm delivers a torque of 240 N.m to an Output Shaft that is rotating @ 200 rev/min.

a. if the efficiency of the machine is 70%, compute the Output Torque

b. what is the Output Power?

when I follow your post for part a, I get:

.7= 200T(torque)/(240 x 600)
.7= 200T/144000
.7 x 144000 = 200T
100800 = 200T
T=504 N.m

for part b I get
.7 x 3 x 240 = 504

what am I missing? besides a brain??

a. To = 240 * 800/200 * 0.7 = 672N.m