Calculating Bulb Switched-On Duration

The problem asks us to find the total time duration for which a bulb remained switched on. We are given the exact time it was switched on and the exact time it was switched off on the same day.

To find the duration, we need to subtract the start time from the end time.

• Bulb Switched On: 02 hours 39 minutes 40 seconds
• Bulb Switched Off: 12 hours 30 minutes 34 seconds

We will perform subtraction column by column, starting from seconds, then minutes, and finally hours.

Step 1: Subtracting Seconds

We need to subtract 40 seconds from 34 seconds. Since 34 is less than 40, we need to borrow from the minutes column. We borrow 1 minute (which is equal to 60 seconds) from the 30 minutes in the end time.

• End time seconds: $34 + 60 = 94$ seconds
• End time minutes become: $30 - 1 = 29$ minutes

Now, subtract the seconds:

$94 \text{ seconds} - 40 \text{ seconds} = 54 \text{ seconds}$

Step 2: Subtracting Minutes

After borrowing, the end time minutes are 29. We need to subtract 39 minutes from 29 minutes. Since 29 is less than 39, we need to borrow from the hours column. We borrow 1 hour (which is equal to 60 minutes) from the 12 hours in the end time.

• End time minutes: $29 + 60 = 89$ minutes
• End time hours become: $12 - 1 = 11$ hours

Now, subtract the minutes:

$89 \text{ minutes} - 39 \text{ minutes} = 50 \text{ minutes}$

Step 3: Subtracting Hours

After borrowing, the end time hours are 11. We subtract the start time hours from this value.

$11 \text{ hours} - 02 \text{ hours} = 09 \text{ hours}$

Final Result

Combining the results from each step, the total duration the bulb was switched on is:

09 hours 50 minutes 54 seconds

This matches one of the given options.

Revision Table: Time Calculations

Additional Information: Calculating Duration

When calculating the duration between two points in time on the same day, you subtract the earlier time from the later time. If the seconds or minutes value in the earlier time is greater than the corresponding value in the later time, you need to 'borrow' from the next higher unit. Remember that borrowing 1 minute adds 60 seconds, and borrowing 1 hour adds 60 minutes. If the time crosses midnight, the calculation involves adding the duration from the start time to midnight and the duration from midnight to the end time on the next day.