Question

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

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

Hint:

For uniformly gaining clocks, equate gain to elapsed time × gain rate. Convert all into consistent units (seconds).

Answer 1

The Correct Option is B

Total gain = \(2 \text{ min} + 4 \text{ min } 48 \text{ sec} = 6 \text{ min } 48 \text{ sec} = 408 \text{ seconds}\) Time duration = from Monday noon to next Monday 2 p.m. = 7 days + 2 hours = 170 hours = 612,000 seconds Rate of gain = \(\frac{408}{612000} = \frac{1}{1500}\) seconds per second Let \(t\) seconds be the time from Monday noon when the watch was correct. Then error = \(t \times \frac{1}{1500}\) = time gained = should be zero at that point So, \[ \text{Watch is correct when it has gained 2 minutes (120 seconds)} \] \[ \frac{t}{1500} = 120 \Rightarrow t = 180000 \text{ seconds} = 50 \text{ hours} \Rightarrow 2 p.m. Wednesday \] \fbox{Final Answer: (B) 2 p.m. on Wednesday}