If it is exactly noon hour, the Clock hands are overlapped, that is, they are exactly aligned on top of each other. The question is: how long does it take for the two hands to overlap again in the next turn?
Note that in the 12 hours after 12 noon, the clock hands pass each other 11 times until they meet again at 12 midnight
So....that means that they pass each other every 12 / 11 ths hours...
So....in terms of minutes ...... 12/11 * 60 ≈ 65.45 minutes = 65 minutes and [ .45 *60 ] seconds ≈
65 minutes and 27 seconds
So....they meet again at about 27 seconds after 1:05 PM