What other time (or times) could it have been?

Question

It was the middle of the winter in Scandinavia, and the poor boy, sick with a cold, was lying in bed. He woke up in the night, but he knew that the night lasted from 3:00 P.M. to 9:00 A.M. at that time of year. The boy wearily glanced at his clock and, thinking it said 4:42, buried his head back in the pillow. But as he fell asleep he realized he hadn't distinguished the hour hand from the minute hand. If it wasn't 4:42 in the morning.

What other time (or times) could it have been?

Answer 1

WE have to reverse time hour and minute hand in 04:42,,, its obvious that hour hand will be bet 8 and 9 so our answer wil be 8 hours 20 minutes + ( something )
12 hrs = 360 degrees
we know 60min=30 degree
1 min = .5 degrees
= = = = =42 min= 21 degrees

===== at 04:42 hours hand moves 21 degrees further down

Now consider the reverse case
now between 20 minutes to 25 minutes we have 30 degrees

 === ==       30 degrees = 5min
       == ==    21 degrees = (5/30)*21 = 3.5 minutes

hence our answer is 08:23:30 , or 8 hours 23 minutes 30 seconds

so if it is 4:42 pm then ans is 8:23:30 pm and it it is 4:42 am ans is 8:23:30 am