Question

At what time between 5 and 6 O'clock, will the hands of a clock be at an angle of 62°?​

Answer 1

Answer:

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Answer 2

Answer:

555hours

$5 \: hours \: 17 \times \frac{2}{11}$

and

$5hours \: 38 \times \frac{6}{11}$

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)