# At what time between 5 and 6 O'clock, will the hands of a clock be at an angle of 62°?   Option 1)   5 hours    Option 2)   5 hours     Option 3)   5 hours 16 minutes   Option 4)   Both (2) and (3)   Option 5)   None of these

We know that In 60 Minutes,

Minute hand covers 360 degrees.

Hour hand covers 30 degrees.

In every 60 Min Minute hand covers 330 degrees more than the hour hand.

330 degree in minutes = 55 Minutes

So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.

To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11

Case 1 - When the minute hand is behind

The distance while there will be time 5 'o' clock = 25 minutes or 150 degree

distance to be cover to make 62 degrees = 150-62 => 88 degree or 44/3 min

time taken after 5 = 44/3 x 12/11 => 16 minute

So the exact time when the hands will be together = 3: 16

Case-2 When the minute hand is ahead

The distance while there will be time 5 'o' clock = 25 minutes or 150 degree

distance to be cover to make 62 degrees = 150+62 => 212 degree or 106/3 min

time taken after 5 = 106/3 x 12/11 => 38 (6/11) minute

So the exact time when the hands will be together = 3: 38 (6/11)

Thus, Option(4) will be the answer.

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