In every 30 minutes the time of a watch increases by 3 minutes. After showing the correct time at 5 a.m; what time will the watch show after 6 hours?

### Concept & Rate of Gain The watch is running fast. We need to find the total time gained over the given period and add it to the actual elapsed time. Gain per given interval: 3 minutes gained per 30 minutes. ### Step-by-Step Solution 1. **Determine the rate of gain:** In 30 minutes, the watch gains 3 minutes. Therefore, in 60 minutes (1 hour), the watch gains $3 \times 2 = 6$ minutes. 2. **Calculate total gain for the period:** The elapsed time is 6 hours. Total time gained in 6 hours = $6 \text{ hours} \times 6 \text{ minutes/hour} = 36 \text{ minutes}$. 3. **Calculate the displayed time:** Actual time after 6 hours from 5:00 a.m. is $5 + 6 = 11:00 \text{ a.m.}$ The watch will show the actual time plus the gained time. Time shown = 11:00 a.m. + 36 minutes = 11:36 a.m. ### Exam Strategy & Shortcut Find the hourly gain ($6$ mins/hr) and multiply by total hours ($6$ hrs) to get $36$ mins. Add this directly to the $6$ hours elapsed from $5$ a.m. ($11:00$ a.m. + $0:36$ = $11:36$ a.m.). ### Common Pitfall Some students might subtract the gained time instead of adding it, or incorrectly calculate the rate (e.g., assuming it gains 3 mins an hour). ### Final Answer Therefore, the correct answer is **11 : 36 a.m.**