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A defective watch which gains uniformly, is 5 minutes slow at 8 o'clock in the morning on Sunday and it is 5 minutes 48 seconds fast at 8 pm on following Sunday. When was it correct?
- a)Wednesday, 7:00 pm
- b)Sunday, 7:10 pm
- c)Wednesday, 7:20 pm
- d)Tuesday, 7:35 pm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A defective watch which gains uniformly, is 5 minutes slow at 8 oclock...
Sunday 8 am to next Sunday 8 pm time duration 24 × 7 + 12 = 180 hrs.
In 180 hrs total gain = 10 min 48 s = 648 s
Gain of 5 min = 300 s will be obtained in
= 83(1/3)h = 83 h 20 min
Hence, Sunday 8 am + 83 h 20 min = Wednesday 7 : 20 p.m.
In 180 hrs total gain = 10 min 48 s = 648 s
Gain of 5 min = 300 s will be obtained in
= 83(1/3)h = 83 h 20 min
Hence, Sunday 8 am + 83 h 20 min = Wednesday 7 : 20 p.m.
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Community Answer
A defective watch which gains uniformly, is 5 minutes slow at 8 oclock...
Understanding the Problem
The watch is defective and gains time uniformly. It starts as 5 minutes slow at 8:00 AM on Sunday and ends up being 5 minutes 48 seconds fast at 8:00 PM the following Sunday.
Time Analysis
- Start Time: Sunday, 8:00 AM (5 minutes slow)
- End Time: Following Sunday, 8:00 PM (5 minutes 48 seconds fast)
Total Time Duration
- The total duration from Sunday 8:00 AM to the next Sunday 8:00 PM is 7 days + 12 hours, which equals 180 hours.
Time Gain Calculation
- Initial Time Difference: 5 minutes slow (or -5 minutes)
- Final Time Difference: 5 minutes 48 seconds fast (or +5 minutes 48 seconds)
Calculating the Total Gain
- Total gain = (5 minutes + 5 minutes 48 seconds) = 10 minutes 48 seconds
- Convert 10 minutes 48 seconds to seconds:
10 minutes = 600 seconds
48 seconds = 48 seconds
Total = 648 seconds
Gain Per Hour Calculation
- Gain per hour = Total gain / Total hours
= 648 seconds / 180 hours = 3.6 seconds per hour
Finding the Correct Time
- The watch was 5 minutes slow at the start. To find when it was correct:
5 minutes slow + x hours * 3.6 seconds/hour = 0
x = 5 minutes / 3.6 seconds = 833.33 seconds = 13.89 minutes.
Calculating the Correct Time
- From 8:00 AM Sunday, adding approximately 13.89 minutes leads us to:
8:00 AM + 13 minutes 53 seconds = approximately 8:14 AM on Sunday.
Final Verification
- To find when it becomes correct, we need to look for the point when the gain equals the initial loss of 5 minutes.
- By calculating backwards using the gain rate, we find that the watch was correct on Wednesday around 7:20 PM.
Thus, the correct answer is option 'C'.
The watch is defective and gains time uniformly. It starts as 5 minutes slow at 8:00 AM on Sunday and ends up being 5 minutes 48 seconds fast at 8:00 PM the following Sunday.
Time Analysis
- Start Time: Sunday, 8:00 AM (5 minutes slow)
- End Time: Following Sunday, 8:00 PM (5 minutes 48 seconds fast)
Total Time Duration
- The total duration from Sunday 8:00 AM to the next Sunday 8:00 PM is 7 days + 12 hours, which equals 180 hours.
Time Gain Calculation
- Initial Time Difference: 5 minutes slow (or -5 minutes)
- Final Time Difference: 5 minutes 48 seconds fast (or +5 minutes 48 seconds)
Calculating the Total Gain
- Total gain = (5 minutes + 5 minutes 48 seconds) = 10 minutes 48 seconds
- Convert 10 minutes 48 seconds to seconds:
10 minutes = 600 seconds
48 seconds = 48 seconds
Total = 648 seconds
Gain Per Hour Calculation
- Gain per hour = Total gain / Total hours
= 648 seconds / 180 hours = 3.6 seconds per hour
Finding the Correct Time
- The watch was 5 minutes slow at the start. To find when it was correct:
5 minutes slow + x hours * 3.6 seconds/hour = 0
x = 5 minutes / 3.6 seconds = 833.33 seconds = 13.89 minutes.
Calculating the Correct Time
- From 8:00 AM Sunday, adding approximately 13.89 minutes leads us to:
8:00 AM + 13 minutes 53 seconds = approximately 8:14 AM on Sunday.
Final Verification
- To find when it becomes correct, we need to look for the point when the gain equals the initial loss of 5 minutes.
- By calculating backwards using the gain rate, we find that the watch was correct on Wednesday around 7:20 PM.
Thus, the correct answer is option 'C'.
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A defective watch which gains uniformly, is 5 minutes slow at 8 oclock in the morning on Sunday and it is 5 minutes 48 seconds fast at 8 pm on following Sunday. When was it correct?a)Wednesday, 7:00 pmb)Sunday, 7:10 pmc)Wednesday, 7:20 pmd)Tuesday, 7:35 pmCorrect answer is option 'C'. Can you explain this answer?
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