Multiple choice

The minute hand of a clock crosses the hour hand x minutes past 7 in the evening. Some guests come 20 minutes later. At what time do the guests come?

  1. 7:58:11 pm

  2. 7:10:27 pm

  3. 7:45:15 pm

  4. None of these
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A Correct answer
Explanation

At 7:00, the minute hand is 35 minute spaces behind the hour hand. Since the minute hand gains 55 minute spaces over the hour hand every 60 minutes, it will overtake the hour hand at 35 * (60/55) = 38 and 2/11 minutes past 7. Adding 20 minutes to this gives 58 and 2/11 minutes past 7, which is approximately 7:58:11 pm.

AI explanation

Using the formula for overlapping hands, M equals 60H divided by 11, we substitute H equal to 7. This gives M equal to 420 divided by 11, which is 38 and 2/11 minutes past 7. The guests arrive 20 minutes later, so we add 20 to 38 and 2/11, resulting in 58 and 2/11 minutes past 7. Converting 2/11 of a minute to seconds gives approximately 11 seconds, making the arrival time 7:58:11 p.m.

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