Between 2 & 3 o'clock what is the time when the hour and minute hand are in the same position ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Let the time when the hour and the minute hand are in the same position between 2 o'clock and 3 o'clock be at T minutes past 2.

The hour hand moves 360/12 = 30 degrees in an hour. At 2, the hour hand makes an angle of 60 degrees with the line pointing towards 12.

At T past 2, the angle made by the hour hand with line pointing towards 12 is 30 + (30/60)*T. The angle made by the minute hand is (360/60)*T

As the two have to be at the same position, 30 + T/2 = (360/60)*T

=> 30 + T/2 = 6T

=> 11T/2 = 30

=> T = 60/11

=> T = 5.45

The time when the two hands are at the same position is 5.45 minutes past 2.

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