Multiple choice

A watch which gains uniformly is 3 minutes slow at noon on Monday and is 3 minutes 48 seconds fast at 2 p.m. on the following Monday. At what time will the clock show the correct time?

  1. $2$ p.m. On Tuesday
  2. $2$ p.m. On Wednesday
  3. $3$ p.m. On Thursday
  4. $1$ p.m. On Friday
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C Correct answer
Explanation

The total time from Monday noon to the following Monday 2 p.m. is 7 days and 2 hours = 170 hours. The watch gained 3 minutes + 3 minutes 48 seconds = 6.8 minutes. To show the correct time, it must gain 3 minutes. The time taken is (3 / 6.8) * 170 hours = 75 hours. 75 hours is 3 days and 3 hours. Monday noon + 3 days 3 hours = Thursday 3 p.m.

AI explanation

The watch goes from being 3 minutes slow to being 3 minutes and 48 seconds (3.8 minutes) fast over exactly 7 days (168 hours), meaning it gained a total of 6.8 minutes. To find the hours it takes for the watch to gain the initial 3 minutes required to show the exact correct time, we calculate (3 / 6.8) multiplied by 168 hours, which equals 74.117 hours. Adding this time to noon on Monday results in 3 p.m. on Thursday.

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