At what time between 3 and 4 O'clock are the hands of a clock in the opposite direction?

 

  • Option 1)

     

    3 hours  48\frac{6}{11}\; minutes

     

  • Option 2)

     

    3 hours   49\frac{1}{11}\; minutes

     

  • Option 3)

     

    3 hours  50\frac{4}{11}\; minutes

     

  • Option 4)

     

    none of these

     

  • Option 5)

     

    3 hours  47\frac{2}{11}\; minutes

     

Answers (1)

We know that In 60 Minutes,

Minute hand covers 360 degrees.

Hour hand cover 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

At 3 'o' clock,

The distance between the minute hand and hour hand = 15 Minute

Distance to be covered to be straight-line = 45 Minute

time taken after 3 = 45 x 12/11 => 49 (1/11)

So the exact time when the hands will be together = 3: 49 (1/11)

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