In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach Physics and Mathematics. How many teach Physics?

In a school, there are 30 teachers who teach Mathematics or Physics. Of these, 18 teach Mathematics and 6 teach both Physics and Mathematics. How many teach Physics only?

Out of 80 students who secured first class marks in Matchematics or in Physics , 50 obtained first class marks in Mathematics and 10 in both Physics and Mathematics. How many students secured first class marks in Physics only ?

Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 teach Physics and 7 teach Chemistry. 4 teachers both Mathematics and Physics but none teaches both Mathematics and Chemistry. What is the number of teachers who teach both Chemistry and Physics ?

In a class, 22 students offered Mathematics, 18 students offered Chemistry and 24 students offered Physics. All of them have to offer at least one of these. 11 are in both Mathematics and Chemistry, 13 in Chemistry and Physics and 14 in Mathematics and Physics and 7 have offered all the three subjects. Find : how many students are there in the class ?

A class has 175 students. The following is the description showing the number of students studying one or more of following subjects in this class. Mathematics 100 , Physics 70, Chemistry 46, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18 : Find : the number of students who are enrolled in Mathematics alone, Physics alone and Chemistry alone .

In a class, 22 students offered Mathematics, 18 students offered Chemistry and 24 students offered Physics. All of them have to offer at least one of these. 11 are in both Mathematics and Chemistry, 13 in Chemistry and Physics and 14 in Mathematics and Physics and 7 have offered all the three subjects. Find : how many students offered only Mathematics ?

In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry , 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.

75 students secured first division marks either in English or in Mathematics or in both. If 50 of them secured first division in Mathematics and 10 in both English and Mathematics, then how many got first division in English ?

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had takes Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all three subjects. Find the number of students that had taken : Physics and Chemistry but not Mathematics.

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had takes Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all three subjects. Find the number of students that had taken : Mathematics and Physics but not Chemistry.