Dr. DoLittle always goes walking to the clinic and takes the
same time while going and while coming back. One day he
noticed something.
When he left the home, the hour hand and the minute hand
were exactly opposite to each other and when he reached the
clinic, they were together.
Similarly, when he left the clinic, the hour hand and the
minute hand were together and when he reached the home, they
were exactly opposite to each other.
How much time does Dr. DoLittle take to reach home from the
clinic? Give the minimal possible answer.
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32 minutes 43.6 seconds
In twelve hours, the minute hand and the hour hand are
together for 11 times. It means that after every 12/11
hours, both the hands are together.
Similarly in twelve hours, the minute hand and the hour hand
are exactly opposite to each other for 11 times. It means
that after every 12/11 hours, both the hands are opposite.
Now, let's take an example. We know that at 12 both the
hands are together and at 6 both the hands are exactly
opposite to each other.
After 6, both the hands are in opposition at [6+(12/11)]
hours, [6+2*(12/11)] hours, [6+3*(12/11)] hours and so on.
The sixth such time is [6+6*(12/11)] hours which is the
first time after 12. Thus after 12, both the hands are
opposite to each other at 12:32:43.6
Hence, Dr. DoLittle takes 32 minutes and 43.6 seconds to
reach home from the clinic.
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