There is an alien planet where a week comprises of eight days - Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Funday. One day comprises of 36 hours and every hour comprises of 90 minutes while every minutes has 60 seconds. We know that on earth, the hour hand covers the whole dial twice every day.
Can you find out what is the angle between the hands of the clock on the alien planet when the time is 15:40 am?
Solution:
Since there are 36 hours in a day, we can fairly say that the clock will be having 18 hours.
Now those 18 hours must cover 360 degrees
So, 1 hour covers 20 degrees
And 15 hours cover 15*20 = 300 degrees
Now
1 hour = 90 minutes
Thus it takes 90 minutes for the hour hand to turn 20 degrees
For 1minutes hour hand goes 2/9 degrees
For 40 minutes hour hand will go (2/9) * 40 degrees = 80/9 degrees =9 degrees (approx.)
Hence the hour hand at 15:40 AM covers total of 300+9 = 309 degrees
Now as 90 minutes = 360 degrees (or 1 minute = 4 degrees)
The minute hand covers = 40*4 = 160 degrees
Therefore the angle between these hands = 309 - 160 = 149 degrees