(a) The boat sinks a little more in water so that the weight of new volume of water displaced by the boat equalizes the weight of the boat and the boy.
(b) The weight of the water displaced by submerged part of the boat increases. It is now equal to sum of weight of boy and weight of boat.
(c) The buoyant force acting on the boat increases. The new buoyant force is equal to sum of weight of boy and weight of boat.