Multiple choice

At what time, between 3 o'clock and 4 o'clock, both the hour hand and minute hand coincide each other?

  1. 3:16 7/11

  2. 3:16 11/4

  3. 3:30

  4. 3:16 4/11

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 3 o'clock, the hands are 15 minutes apart. The minute hand gains 5.5 degrees per minute on the hour hand. To coincide, the minute hand must cover the 15-minute gap. Time = 15 / (11/60) = 900/11 = 81 9/11 minutes past 12, but we need the time past 3. The formula is (60/11) * H. At 3, it is (60/11) * 3 = 180/11 = 16 4/11 minutes past 3.

AI explanation

Using the formula for coinciding hands, the time is 60 multiplied by the hour number divided by 11 minutes past the hour. For hour 3, this is 180/11 minutes past 3 o'clock. Converting the improper fraction gives 16 and 4/11 minutes, so the hands coincide at 3:16 4/11.

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