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At what time immediately prior to Six O'clock the hands of
the clock are exactly opposite to each other. Give the exact
time in hours, minutes and seconds.
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Answer / guest
It is obvious that between 5 O'clock and 6 O'clock the hands
will not be exactly opposite to each other. It is also
obvious that the hands will be opposite to each other just
before 5 O'clock. Now to find exact time:
The hour hand moves 1 degree for every 12 degrees that the
minute hand moves. Let the hour hand be X degree away from 5
O'clock. Therefore the minute hand is 12X degree away from
12 O'clock.
Therefore solving for X
Angle between minute hand and 12 O'clock + Angle between 12
O'clock and 4 O'clock + Angle between 4 O'clock and hour
hand = 180
12X + 120 + (30-X) = 180
11X = 30
Hence X = 30/11 degrees
(hour hand is X degree away from 5 O'clock)
Now each degree the hour hand moves is 2 minutes.
Therefore minutes are
= 2 * 30/11
= 60/11
= 5.45 (means 5 minutes 27.16 seconds)
Therefore the exact time at which the hands are opposite to
each other is
= 4 hrs. 54 min. 32.74 seconds
| Is This Answer Correct ? | 17 Yes | 8 No |
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