Fig. below shows an epicyclic gear in which the wheel P, having 45 teeth of 5/8 in. pitch, is geared
with Q through the intermediate wheel R at the end of the arm A. When P is rotating at 63 r.p.m. in a
clockwise direction, and A is rotating at 9 r.p.m., also in a clockwise direction, the wheel Q is required to
rotate at 21 r.p.m. in an anticlockwise direction. Find the necessary numbers of teeth in Q and R, and the
P.C.D. of Q.