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

Options

A. `10:54`a.m
B. `11:30` a.m
C. `11:36` a.m
D. `11:42` a.m

Answer

To solve the problem step by step, we need to determine how much time the faulty watch will show after 6 hours, given that it gains time every 30 minutes.

### Step 1: Understand the gain of the watch
The watch gains 3 minutes for every 30 minutes of actual time.

### Step 2: Calculate the gain per hour
Since there are 60 minutes in an hour, we can find the gain in one hour:
- In 30 minutes, the watch gains 3 minutes.
- Therefore, in 60 minutes (which is 2 times 30 minutes), the watch will gain:
\[ 3 \text{ minutes} \times 2 = 6 \text{ minutes} \]

### Step 3: Calculate the total time gain over 6 hours
Now, we need to find out how much time the watch will gain over 6 hours:
- In 6 hours, the total gain will be:
\[ 6 \text{ minutes/hour} \times 6 \text{ hours} = 36 \text{ minutes} \]

### Step 4: Determine the correct time after 6 hours
Starting from the correct time of 5 a.m., we add 6 hours:
- 5 a.m. + 6 hours = 11 a.m.

### Step 5: Add the gained time to the displayed time
Now, we add the 36 minutes gained by the watch to the time shown:
- 11:00 a.m. + 36 minutes = 11:36 a.m.

### Conclusion
Therefore, after 6 hours, the watch will show **11:36 a.m.**.

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