Answer : First, he should measure how long it takes for the liquid to become clear if X and Y are mixed together. Then, he should measure how long it takes if he also adds substance A to X and Y. He will find out if substance A is a catalyst
Explanation : Measuring the time taken for the liquid to become clear when X and Y were mixed together will give an assumption about the reaction time and the rate of reaction.
Then same measurement should be done when the substance A is added to the liquid of X and Y mixture. If there is a fast reaction that occurs when A is added to the reaction mixture then it can be concluded that A acts as an catalyst for mixing X with Y. Also, by comparing the reaction rates of both the reaction it can be easily concluded that A was a catalyst or not.