Answer :
Using proportions, it is found that the correct time when it reads 10:30pm is of 9:40 pm.
What is a proportion?
A proportion is a fraction of total amount, and the measures are related using a rule of three.
In this problem, when 56 minutes have passed, the clock indicates that 60 minutes have passed. Hence, what is the time passed when the clock indicates that 12 hours and 30 minutes, that is, 60 x 12 + 30 = 750 minutes have passed?
Hence, the rule of three is:
56 minutes - 60 minutes
x minutes - 750 minutes
Applying cross multiplication:
[tex]60x = 56 \times 750[/tex]
[tex]x = \frac{56 \times 750}{60}[/tex]
[tex]x = 700[/tex]
700 minutes is 660/60 = 11 hours + 40 minutes after 10:00 am, hence the correct time is of 9:40 pm.
You can learn more about proportions at https://brainly.com/question/24372153