A watch gains 5 seconds every 3 hours. It was set right on Monday at 8 AM. What time will it show on the following Friday at 8 PM?

The watch was set on Monday at 0545 hours.
The time to determine is on the following Friday at 1945 hours.

• From Monday 0545 to Tuesday 0545 = 24 hours

• From Tuesday 0545 to Wednesday 0545 = 24 hours

• From Wednesday 0545 to Thursday 0545 = 24 hours

• From Thursday 0545 to Friday 0545 = 24 hours Total for full days = $4 \times 24 \text{ hours} = 96 \text{ hours}$.

• Remaining time on Friday: From Friday 0545 to Friday 1945.

  $$19 \text{ hours } 45 \text{ minutes} - 5 \text{ hours } 45 \text{ minutes} = 14 \text{ hours}$$

• Total duration = $96 \text{ hours} + 14 \text{ hours} = 110 \text{ hours}$.

The watch loses half a minute (0.5 minutes) every hour.
Total time lost = Total duration $\times$ Loss rate per hour

$$110 \text{ hours} \times 0.5 \text{ minutes/hour} = 55 \text{ minutes}$$

The actual time is Friday, 1945 hours.
Subtract 55 minutes from 1945 hours:

$$19 \text{ hours } 45 \text{ minutes} - 55 \text{ minutes}$$

To subtract 55 minutes from 45 minutes, we borrow 1 hour (60 minutes) from the hours.

$$18 \text{ hours } (45 + 60) \text{ minutes} - 55 \text{ minutes}$$ $$18 \text{ hours } 105 \text{ minutes} - 55 \text{ minutes}$$ $$18 \text{ hours } (105 - 55) \text{ minutes}$$ $$18 \text{ hours } 50 \text{ minutes}$$

So, the watch will show Friday, 1850 hours.

1850 hours is in the 24-hour system.
To convert to 12-hour system for times greater than 12, subtract 12 from the hour.

$$18 - 12 = 6$$

The time is 6:50 PM.

The watch will show Friday, 6:50 PM.

The time the watch will show on the following Friday at 1945 hrs is $\boxed{\text{Friday, 6:50 PM}}$.