Multiple choice

A watch which gains 10 seconds in 5 minutes was set correct at 9 a.m. When the watch indicates 20 minutes past 7 O'clock the same evening, the true time is

  1. 7 p.m.

  2. 7.40 p.m.

  3. 7.10 p.m.

  4. 8 p.m.
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A Correct answer
Explanation

The watch gains 10 seconds in 5 minutes, which is 2 seconds per minute. In 1 hour (60 mins), it gains 120 seconds (2 minutes). The watch shows 7:20 p.m. starting from 9 a.m., which is 10 hours and 20 minutes = 620 minutes. The watch gains 2 seconds for every 60 seconds of true time, so it runs at a ratio of 62/60. True time = 620 * (60/62) = 600 minutes. 600 minutes = 10 hours. 9 a.m. + 10 hours = 7 p.m.

AI explanation

When the watch indicates 7:20 pm, it has counted 10 hours and 20 minutes, or 620 minutes, since 9 am. The ratio of real time to watch time is 290 to 295, since the watch counts 295 seconds for every 290 real seconds. Multiplying 620 minutes by (290 / 295) gives a real elapsed time of 600 minutes. Adding 600 minutes, which is 10 hours, to 9 am results in a true time of 7 pm.

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