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(#M40013750) SELF question Keep an EYE

Find the time between 1500 hours and 1600 hours, when angle between both the hands is 180.

Amit kumar (12 years ago)

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Vinay Sipani   (12 years ago)

15 : 49 + 60/11 seconds

It can be assumed that the minute hand will be b/w 9 and 10 as hour hand will be b/w 3 and 4.

If second hand moves one second i.e 6 deg ,minute hand moves (1/10) deg => hour hand moves (1/120) deg.
If minute hand moves 1 minute i.e 6 deg , hour hand moves (1/2) deg.
=> after 45 min have passed, hour hand has moved by (45/2) = 22.5 deg

The angle of hour hand from 3 must be equal to angle min hand from 9 so that angle b/w them = 180
Let t be the number of seconds that second hand has moved after 15:45

=> 22.5 + (t/120) = (t/10)
=> t = 2700/11 seconds
=> time when two hands are at 180 deg = 15: 45 + (2700/11)
= 15:49 , (60/11) seconds

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