Kumbhakarna starts sleeping between 1 pm and 2 pm and he wakes up when his watch shows such a time that the two hands (i.e., hour-hand and minute-hand) interchange the respective places. He wakes up between 2 pm and 3 PM on the same night. How long does he sleep ?
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Answer:
55 Mins
Step-by-step explanation:
Kumbhakarna starts sleeping between 1 pm and 2 pm and he wakes up when his watch shows such a time that the two hands (i.e., hour-hand and minute-hand) interchange the respective places. He wakes up between 2 pm and 3 PM on the same night.
Kumbhakarna starts sleeping between 1 pm and 2 pm
so Hour hand between 1 & 2
He wakes up between 2 pm and 3 PM
so now Hour Hand is Between 2 & 3 & minute Hand is between 1 & 2
( as Minute & hour hand interchanged their position)
Hence Minute hand should be between 2 & 3 Between ( 1 - 2 pm)
for every 360° rotation(60 minutes) of minute hand hour hand moves 30°
=> for every 12° rotation (1 minutes) of minute hand hour hand moves 1°
Minute hand between 2 & 3 Means ( 60° to 90°)
Hence hour hand = ( 5° to 7.5°) after 1 PM (30 °)
Let say minute hand is at 60° + x° ( x < 30°)
then hour hand = 5° + (x/12)° after 1 PM (30 °)
= 35° + (x/12)°
This mean minute hand will move
360° - (60° + x°) + 35° + (x/12)° to reach earlier Hour hand
= 335° + 11x/12°
This movement means Hour hand will move
= (335° + 11x/12°)/12
Hour hand will move from 35° + (x/12)° to 60° + x°
= (25 + 11x/12)°
Equating hour hand movement
(335° + 11x/12°)/12 = (25 + 11x/12)°
=> 335° + 11x/12° = 300 + 11x
=> 35° = 121x/12
=> x = 3.47°
3.47° = 0.58 minutes
Initial position was 1 PM 10.58 minutes
Final position was 2PM 5.88 minutes
He slept around 55.3 minutes
If We take it simple
Then he slept at 1 : 10 PM
& waked up at 2: 05 PM
Slept for 55 Mins