A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day when the watch indicated quarter past 4 O’clock, the true time is
Question
A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day when the watch indicated quarter past 4 O’clock, the true time is
Solution
The watch gains 5 seconds every 3 minutes. This means it gains 1 second every 36 seconds (since 3 minutes = 180 seconds and 180/5 = 36).
From 7 am to 4:15 pm is 9 hours and 15 minutes, which is 555 minutes or 33,300 seconds.
During this time, the watch would have gained an extra 33,300/36 = 925 seconds, which is approximately 15 minutes and 25 seconds.
So, when the watch reads 4:15 pm, the true time would be 15 minutes and 25 seconds earlier, which is approximately 4:00 pm.
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