Understanding the Faulty Watch Problem

This question deals with a common type of time and clock problem where a watch is running incorrectly. In this specific case, the watch loses a fixed amount of time every hour. To solve this, we need to figure out how much total time the watch needs to lose to catch up to the correct time cycle again.

Key Concept: Resetting the Time Cycle

A standard watch operates on a 12-hour cycle (showing 1 through 12). For a faulty watch that is consistently losing time to show the correct time again, it must have lost a total duration equal to a full cycle or a multiple of a full cycle. Since the watch dial goes from 1 to 12, losing 12 hours means it has gone through one complete rotation behind the actual time, thus showing the correct time momentarily.

Therefore, the watch will show the correct time again when it has lost a total of 12 hours relative to the correct time.

Step-by-Step Calculation

Let's break down the problem and calculate when the watch shows the correct time.

• The watch loses 5 minutes every hour.
• To show the correct time again, the watch must lose 12 hours.
• First, convert the total required loss into minutes:

Total loss needed = 12 hours

Total loss needed in minutes = $12 \text{ hours} \times 60 \text{ minutes/hour} = 720 \text{ minutes}$.

• Now, calculate the time it takes for the watch to lose these 720 minutes.
• The watch loses 5 minutes in 1 hour.
• Time taken to lose 1 minute = $\frac{1 \text{ hour}}{5 \text{ minutes}}$.
• Time taken to lose 720 minutes = $720 \text{ minutes} \times \frac{1 \text{ hour}}{5 \text{ minutes}}$.

Time taken = $\frac{720}{5} \text{ hours} = 144 \text{ hours}$.

• The watch will show the correct time again after 144 hours from when it was set right.
• Now, we need to convert these hours into days to find the specific date and time.
• There are 24 hours in a day.

Number of days = $\frac{144 \text{ hours}}{24 \text{ hours/day}} = 6 \text{ days}$.

• The watch was set right at 6 a.m. on a Monday.
• Adding 6 days to Monday:

After 6 full days (144 hours), the day will be Sunday, and the time will be 6 a.m.

Conclusion

The watch will show the correct time again at 6 a.m. on the next Sunday after it was set right on Monday.

Revision Table: Watch Time Calculation

Additional Information: Clock Problems

Clock problems in quantitative aptitude often involve calculating the relative speed of the hour and minute hands, determining the angle between them, or dealing with faulty clocks that gain or lose time. Understanding the basic mechanics of a clock is crucial:

• The minute hand completes one full circle (360°) in 60 minutes. Its speed is 6° per minute (360/60).
• The hour hand completes one full circle (360°) in 12 hours. Its speed is 0.5° per minute (360/(12*60)).
• The relative speed of the minute hand with respect to the hour hand is 5.5° per minute (6° - 0.5°).

Problems involving faulty clocks require calculating the total time gained or lost over a specific period and then determining when the clock will show the correct time again, which happens when the total gain or loss equals a 12-hour cycle (or 720 minutes).