Multiple choice

Arjun goes out for some time between 5 o'clock and 6 o'clock and returns between 6 o'clock and 7 o'clock. He notices that the hands of the clock have exactly interchanged their positions. At what approximate time did Arjun go out?

  1. 36 minutes past 5 o'clock

  2. 34 minutes past 5 o'clock

  3. 32 minutes past 5 o'clock

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the time be 5:x and 6:y. The positions of hands interchange. The minute hand at x minutes past 5 is at 6x degrees from 12. The hour hand at y minutes past 6 is at 180 + 0.5y degrees. Solving the system yields approximately 32 minutes.

AI explanation

Let the departure time be 5 hours and X minutes, so the minute hand is at X while the hour hand is at 150 plus X/12 divisions. Since the hands interchange positions upon returning at 6 hours and Y minutes, the equation is X = 30 + Y/12 and Y = 150 + X/12. Solving this system yields X = 31 3/23 minutes. This translates to approximately 32 minutes past 5 o'clock.

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