Final answer:
The watch will show 12:01am at 10pm the same night.
Step-by-step explanation:
To determine the time shown on the watch at 10pm the same night, we need to calculate the number of minutes that have passed from 10am to 10pm. There are 12 hours between 10am and 10pm, and each hour consists of 60 minutes. So, there are a total of 12 x 60 = 720 minutes.
However, the watch has 2 minutes in every 24 hours, which means it gains 2 minutes every day. So, in the 12 hours between 10am and 10pm, the watch would have gained 12/24 x 2 = 1 minute.
Therefore, the total number of minutes shown on the watch at 10pm would be 720 + 1 = 721 minutes. To convert this to hours and minutes, divide 721 by 60 to get 12 hours with a remainder of 1 minute. So, the watch will show 12:01am at 10pm the same night.