 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says, in a group of 400 peoples, 250 can speak Hindi and 200 can speak English. How many can speak both Hindi and English? So first let us learn that if H and E are two finite sets such that they have some common elements, then number of elements in H union E is equal to number of elements in H plus number of elements in E minus number of elements in H intersection E. So this is the key idea. We are going to use in this problem to find how many people can speak both Hindi and English. Start with a solution and let set of Hindi speaking people be denoted by H and set of English speaking people be denoted by E. Then what will H intersection E denote? Yes, set of people who speak both Hindi and English. Now let us find the number of people who speak both Hindi and English by using the key idea which is number of people H union E is equal to number of people who speak Hindi plus number of people who speak English minus number of people who speak both Hindi and English. Now replacing the values number of persons are 400 that is N of H union E is equal to 400, number of persons who speak Hindi are 250 and number of people who speak English are 200. Now substituting the values in the formula we have 400 is equal to 250 plus 200 minus number of people who speak both Hindi and English which is further equal to 400 is equal to 450 minus number of H intersection E which further implies that number of H intersection E is equal to 450 minus 400 which is equal to 50 and so H intersection E is equal to 50 and we can say that number of people who can speak Hindi and English is equal to 50. So this completes the solution hope you enjoyed it take care and have a good day.