Onetrack got it right first time.
The answer is: c. The speed of the water depends on the pressure head, or depth below the free surface. The pressure heads for both outlets are the same, so water speeds are the same. Or we can look at the problem this way: Move the spout around and attach it to the hole. If the water comes out of the downspout fastest it would overwhelm the current from the hole and force its way back into the bucket at B, so you would have a perpetual motion machine with water running from T to B.
If the water comes out of the bottom hole fastest you also have perpetual motion with water flowing the other way. To avoid perpetual motion (and conserve energy), the water flowing out of both the hole and the downspout must have equal speeds.