The ratio of the rotor speeds with the motor operating with 4 and 6 poles respectively can be calculated as follows:

For a 3-phase induction motor, the synchronous speed is given by:

Ns = 120f / p

where Ns is the synchronous speed in RPM, f is the supply frequency in Hz, and p is the number of poles.

For a slip of 0.05, the rotor speed is:

Nr = (1 - s)Ns

where Nr is the rotor speed in RPM.

The ratio of rotor speeds with 4 and 6 poles can be calculated as follows:

Nr_4pole / Nr_6pole = [(1 - s)Ns]_4pole / [(1 - s)Ns]_6pole

Since the supply frequency and slip are the same for both cases, we can cancel them out and the ratio becomes:

Nr_4pole / Nr_6pole = p_6pole / p_4pole

Substituting p_4pole = 4 and p_6pole = 6, we get:

Nr_4pole / Nr_6pole = 6 / 4 = 1.5

Therefore, the ratio of rotor speeds with the motor operating with 4 and 6 poles respectively is 1.5.