Multiple choice

A clock gains 8 minutes every hour. It was correctly set to the current time at 2 PM. On the same day, in the evening, when the clock indicates 7:30 PM, what is the actual, true time?

  1. 8:51 PM

  2. 7:44 PM

  3. 6:51 PM

  4. 6:46 PM

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The clock gains 8 minutes per real hour, so it shows 68 minutes for every 60 actual minutes. From 2:00 PM to the indicated 7:30 PM is 330 clock minutes, corresponding to 330 x 60/68 = about 291 minutes, or 4 hours 51 minutes. The actual time is therefore about 6:51 PM.

AI explanation

The faulty clock shows a total elapsed time of 5 hours 30 minutes (330 minutes) from 2 PM. Since a normal clock has 60 minutes per hour and this clock has 68 minutes for the same period, the ratio of faulty time to true time is 68 to 60. Multiplying the faulty elapsed time of 330 minutes by the fraction 60 / 68 gives a true elapsed time of 291.17 minutes. Adding 291.17 minutes (4 hours 51 minutes) to 2:00 PM results in an actual true time of 6:51 PM.

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