See solution below
Jar A will fill first. This is simply because the diameter of the tap exit by observation is at least four times (4x) more than the diametre of the pipe that connects the jars. I have used the Turquoise (greenish-blue) colour/lines/arrows to show the difference between in pipe daimetre connecting jar A & B compared to that of the tap. See image below:
UPDATED: 20 June, 2019
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