A watch which gains uniformly is 2 minutes low at noon on Monday and i...
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours.
=170 hours.
The watch gains
= (2 + 4 x4/5)min
= 34 / 5 min.in 170 hrs.
Now,34/5 min are gained in 170 hrs.
2 min are gained in(170x 5/34 x2)hrs.
Watch is correct 2 days 2 hrs. after 12 p.m. on Monday
i.e., it will be correct at 2 p.m.on Wednesday.
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A watch which gains uniformly is 2 minutes low at noon on Monday and i...
Analysis:
To solve this problem, we need to determine the time at which the watch is correct, given that it gains uniformly and is 2 minutes slow at noon on Monday and 4 minutes and 48 seconds fast at 2 p.m. on the following Monday.
Step 1: Calculate the total time gained by the watch in one week.
The watch is 2 minutes slow at noon on Monday and 4 minutes and 48 seconds fast at 2 p.m. on the following Monday. This is a time difference of 6 days and 2 hours.
Since the watch gains uniformly, we can calculate the average time gained per day by dividing the total time gained by the number of days.
6 days and 2 hours is equivalent to 146 hours.
There are 24 hours in a day, so the watch gains an average of 6 minutes and 5 seconds per day.
Step 2: Determine the time at which the watch is correct.
Since the watch gains uniformly, we can assume that it gains the same amount of time each day.
If the watch is 2 minutes slow at noon on Monday, it will be 2 minutes + 6 minutes and 5 seconds slow at noon on Tuesday.
To find the time at which the watch is correct, we need to subtract the total time gained from the time at which it was slow.
So, the watch will be correct at noon + (2 minutes + 6 minutes and 5 seconds) on Tuesday.
Step 3: Calculate the final time.
Adding 2 minutes to noon gives us 12:02 p.m., and adding 6 minutes and 5 seconds gives us 12:08:05 p.m.
Therefore, the watch will be correct at 12:08:05 p.m. on Tuesday.
Conclusion:
The watch will be correct at 12:08:05 p.m. on Tuesday. Therefore, the correct answer is option (b) 2 p.m. on Wednesday.