A man stands on the pan of a balance holding a fish in his right hand and bucket of water in his left hand. If he transfers the fish into the bucket, the total weight on the pan

Before transferring the fish, the position is the man with the fish and the bucket of water. After transferring the position is: the man without the fish, but the fish inside the water in the bucket. Thus to know  whether there is any change in weight, it is enough to consider whether there is any change in weight when the fish in air is transferred into the water. The answer is there is no change as when in water though it loses weight due to upthrust of water on it, the level of water increases and exerts an equal force at the bottom.So, (c) is correct.