Answer
Boy: Increases $\omega$
Girl: Can't tell
Work Step by Step
Boy: The boy is on the merry-go-round, so angular momentum will be constant. Thus, when he runs to the center and decreases the moment of inertia, the angular velocity must increase for angular momentum to be conserved.
Girl: She increases angular momentum by applying a torque when she jumps on. However, she also increases the moment of inertia, so we do not have enough information to tell what will happen.
