To solve this question, you need to determine the number of chimes and the time gap between each chime from 1 o'clock to 6 o'clock.
At 1 o'clock, there is 1 chime.
At 2 o'clock, there are 2 chimes.
At 3 o'clock, there are 3 chimes.
At 4 o'clock, there are 4 chimes.
At 5 o'clock, there are 5 chimes.
At 6 o'clock, there are 6 chimes.
The time gap between each chime is 3 seconds.
To calculate the time it takes to know the time after the first chime, you need to add up the time gap between each chime.
For example, to know the time after the first chime at 6 o'clock, you need to add up the time gap between each chime from 1 o'clock to 6 o'clock:
(1-1) + (2-1) + (3-1) + (4-1) + (5-1) + (6-1)
Simplifying this, you get:
(0) + (1) + (2) + (3) + (4) + (5)
Adding these numbers together, you get a sum of 15.
However, this sum does not include the first chime, so you need to add 3 more seconds to account for the time it takes for the first chime to be heard.
Therefore, the total time it takes to know the time after the first chime at 6 o'clock is 15 + 3 = 18 seconds.
Hence, the correct answer is C. 18.