My answer: I think Mr. Ramsay made the bet with Mr. Kelada because he wanted to find out wether his wife cheated on him and got the necklace from a rich lover in New York or not.
Teacher's answer: Mr. Ramsay wanted to prove to Mr. Kelada that he is not really someone who knows everything, a "know-all". After all their arguments, Mr. Ramsay want to win this one.
Inferring - from the fact that Mr. Ramsay and Mr. Kelada argued bitterly. Cause and effect - cause: Mr. Kelada was always sure of himself and argued a lot with Mr. Ramsay. Effect: Mr. Ramsay wanted to win. Uncovering motives