Question

A watch, which gains uniformly, is 2 minutes slow at noon on Monday and is 4 minutes 48 seconds fast at 2 PM on the following Monday. When was it correct?

• A. 2 PM on Tuesday
• B. 2 PM on Wednesday
• C. 3 PM on Thursday
• D. 1 PM on Friday

Hint:

Remember the formula: \( \text{Correction Time} = \frac{\text{Error}_1}{\text{Error}_1 + \text{Error}_2} \times \text{Total Time} \). This shortcut allows you to find the "Correct" moment without calculating the hourly rate.

Answer 1

The Correct Option is B

Concept: Clock problems involving uniform gain or loss are solved by calculating the total time elapsed and the total gain/loss observed.

• Total Time: The duration from the start to the end of the observation.

• Total Gain: The net progress made by the watch from being "slow" to "fast."

Step 1: Calculating the total time and total gain.
Time from Mon Noon to next Mon Noon = 168 hours (7 days). Total Time (until 2 PM) = 168 + 2 =

170 hours. Total Gain = 2 min (slow) + 4 min 48 sec (fast) =

6.8 minutes. (Note: 48 seconds = 48/60 = 0.8 minutes).

Step 2: Finding the time required to show the correct time.
The watch is correct when it gains exactly the

2 minutes it was slow. Time taken = \( \left( \frac{\text{Total Time}}{\text{Total Gain}} \right) \times \text{Initial Loss} \) Time taken = \( \left( \frac{170}{6.8} \right) \times 2 = 25 \times 2 = \textbf{50 hours} \).

Step 3: Determining the specific day and time.
50 hours = 2 days and 2 hours. Monday Noon + 2 days = Wednesday Noon. Wednesday Noon + 2 hours =

2 PM on Wednesday.