At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in \(\left(\frac{60}{55}\times15\right)min. = 16\frac{4}{11}min.\)

So, The hands are coincident at \(16\frac{4}{11}min. past 3\)

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

AM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

PM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes.

  So, The hands coincide 22 times in a day.

In 12 hours, the hands coincide or are in opposite direction 22 times.

So, In 24 hours, the hands coincide or are in opposite direction 44 times a day.

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

So, The watch gains \(\left(2+4\frac{4}{5}\right)min. or \frac{34}{5}min. in 170 hrs\)

Now, \(\frac{34}{5}\)  min. are gained in 170 hrs.

So, 2 min. are gained in \(\left(170\times\frac{5}{34}\times2\right)hrs= 50 hrs.\)

So,Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.