A watch which gains uniformly, is 5 min slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec fast at 8 p.m on following sunday. when was it correct?7pm on wednesday20 min past 7pm on wednesday15min past 7pm on wednesday8pm on wednesday
Question
A watch which gains uniformly, is 5 min slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec fast at 8 p.m on following sunday. when was it correct?7pm on wednesday20 min past 7pm on wednesday15min past 7pm on wednesday8pm on wednesday
Solution
The watch gains time uniformly over a week.
First, let's calculate the total time gained over the week.
The watch was 5 minutes slow at 8 AM on Sunday and 5 minutes 48 seconds fast at 8 PM on the following Sunday.
So, the total time gained is 5 minutes (slow) + 5 minutes 48 seconds (fast) = 10 minutes 48 seconds.
The total time from 8 AM on Sunday to 8 PM on the following Sunday is 7 days * 24 hours/day = 168 hours.
The watch gains 10 minutes 48 seconds over 168 hours.
To find out when the watch showed the correct time, we need to find out when it gained exactly 5 minutes (the time it was initially slow).
We can set up a proportion to solve for this:
10 minutes 48 seconds / 168 hours = 5 minutes / X hours
Solving for X gives us X = 78.26 hours.
This is the amount of time after 8 AM on Sunday when the watch showed the correct time.
78.26 hours is approximately 3 days and 6 hours.
So, the watch showed the correct time at 2 PM on Wednesday.
Therefore, none of the given options are correct.
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