# CAT LRDI Set with Video Solution 05

In a class of 145 students, 70 like Physics, 80 like Chemistry and 90 like Mathematics. Also, 20 like Chemistry only, 30 like both Chemistry and Mathematics but not Physics and 15 like Physics and Mathematics but not Chemistry. It is also known that each of the 145 students likes at least one of the three subjects.
In another class, all the students like Biology only. This class is merged with the previous class to make a new class and as a result now the combined strength of the new class becomes 180. It is also found that in the new class, some of the students from the previous class who like Chemistry or Mathematics but not Physics started liking Biology. As a result, the ratio of number of students who now likeChemistry, Mathematics and Biology to number of students who now like Mathematics and Biology to number of students who like Chemistry and biology becomes 1:3:4.

Question: In the new class, what could be the maximum number of students who like Biology

Question: In the new class, what could be the maximum number of students who like exactly two subjects

Question: In the new class, if the number of students who like Physics and Chemistry only is equal to the number of students who like Mathematics and Biology only then, how many students like exactly three subjects 