A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

In a class of $30$ pupils, $12$ take needle work, $16$ take physics and $18$ take history. If all the $30$ students take at least one subject and no one takes all three then the number of pupils taking $2$ subjects is

In a school there are $20$ teachers who teach mathematics or physics. Of these, $12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics ?

In a committee, $50$ people speak French, $20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

In a class of $100$ students,$15$ students chose only physics (but not mathematics and chemistry),$3$ chose only chemistry (but not mathematics and physics), and $45$ chose only mathematics(but not physics and chemistry). Of the remaining students, it is found that $23$ have taken physics and chemistry,$20$ have taken physics and mathematics, and $12$ have taken mathematics and chemistry. The number of student who chose all the three subjects is