Solution:
If it is 11 o'clock, the clock will chime 10 times after the first chime is heard.
Since the time gap between any two chimes is 2 seconds, this will take 10 × 2 = 20 seconds.

Now, to know what time it really is, you have to wait an 'extra chime gap' to see if the clock chimes again.
Adding the extra 2 seconds, the total time required is 20 + 2 = 22 seconds.

Food for thought:

Does the solution assume that the time taken for the sound of the chime itself is negligible?

Wish to try another puzzle similar in concept to this one? Then click here.