Two ants moving around a circular track

When they meet at 10:00 am, A has covered 60% of the track and B has covered 40% in the same time. Thus, ratio of speeds $v_A : v_B = 60 : 40 = 3 : 2$.

A takes 12 minutes (10:00 am to 10:12 am) to cover the remaining 40% of the track. Therefore, total time taken by A for one full round $= \frac{12}{0.4} = 30$ minutes.

Since speed ratio $v_A : v_B = 3 : 2$, time ratio $T_A : T_B = 2 : 3$. $T_B = \frac{3}{2} T_A = \frac{3}{2} \times 30 = 45\text{ minutes}$

Since A finishes at 10:12 am (30 min after start), start time $t_0 = 9:42$ am. B returns to P at $9:42\text{ am} + 45\text{ minutes} = 10:27$ am.