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?Question 20Answera.20 min past 7pm on wednesdayb.8pm on wednesdayc.7 pm on wednesdayd.15min past 7 pm 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?Question 20Answera.20 min past 7pm on wednesdayb.8pm on wednesdayc.7 pm on wednesdayd.15min past 7 pm on wednesday
Solution
The watch gains uniformly, which means it gains time at a consistent rate.
First, let's calculate the total time gained by the watch.
The watch is 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 by the watch 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 = 10080 minutes.
The watch gains 10 minutes 48 seconds in 10080 minutes.
Let's convert 10 minutes 48 seconds to seconds for easier calculation: 10*60 + 48 = 648 seconds.
So, the watch gains 648 seconds in 10080 minutes.
Now, we want to find out when the watch shows the correct time. This is when the watch has gained exactly 5 minutes (or 300 seconds), because it was initially 5 minutes slow.
We can set up a proportion to solve for this:
648 seconds / 10080 minutes = 300 seconds / x minutes
Solving for x gives us x = (300 * 10080) / 648 = 4657.5 minutes.
Converting 4657.5 minutes to days gives us approximately 3.23 days.
So, the watch shows the correct time about 3.23 days after 8 AM on Sunday, which is around 20 minutes past 7 PM on Wednesday.
So, the answer is a. 20 min past 7pm on Wednesday.
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