Question:medium

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?

Show 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.
Updated On: Jun 30, 2026
  • 2 PM on Tuesday
  • 2 PM on Wednesday
  • 3 PM on Thursday
  • 1 PM on Friday
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Find total elapsed time and total gain.
From Monday noon to the following Monday at 2 PM is $7 \times 24 + 2 = 170$ hours; the watch was 2 min slow at the start and 4 min 48 sec (= 4.8 min) fast at the end, so total gain = $2 + 4.8 = 6.8$ min.
Step 2: Calculate the rate of gain per hour.
Rate = $\frac{6.8}{170} = 0.04$ min per hour.
Step 3: Find when the watch showed the correct time.
At Monday noon the watch was 2 min slow; time needed to gain those 2 min = $\frac{2}{0.04} = 50$ hours from Monday noon; Monday noon + 50 hours = Monday noon + 2 days 2 hours = Wednesday 2 PM.
\[ \boxed{\text{Wednesday 2 PM}} \]
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