Multiple choice

At what time, in minutes, between 3 o'clock and 4'o clock, both the needles will coincide each other?

  1. 16 4/11

  2. 13 4/11

  3. 12 4/11

  4. 5 1/11

  5. None of these
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A Correct answer
Explanation

The hands coincide when the minute hand has gained 3/12 of the circle (15 minutes) plus the movement of the hour hand. The formula is T = (60/11) * H. For H=3, T = 180/11 = 16 4/11 minutes.

AI explanation

At 3 o'clock, the hour hand is 15 minute spaces ahead of the minute hand, and the hands will coincide when the minute hand covers this exact gap. Using the formula for overlapping hands, the minute hand gains 55 minutes in 60 minutes, so the time is 60/55 multiplied by 15. This calculates to 180/11 minutes, which is 16 4/11 minutes past 3.

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