$20$ teachers of a school either teach mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then the number of teachers teaching physics is

In a Mathematics test, the average marks of boys is $x \%$ and the average marks of girls is $y \%$ with $x \neq y$. If the average marks of all students is $z \%$, the ratio of the number of girls to the total number of students is

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 survey it was found that $21$ people liked product $A, 26$ liked product $B$ and $29$ liked product $C.$ If $14$ people liked products $A$ and $B, 12$ people liked products $C$ and $A, 14$ people liked products $B$ and $C$ and $8$ liked all the three products. Find how many liked product $C$ only.

A market research group conducted a survey of $1000$ consumers and reported that $720$ consumers like product $\mathrm{A}$ and $450$ consumers like product $\mathrm{B}$, what is the least number that must have liked both products?

There are $200$ individuals with a skin disorder, $120$ had been exposed to the chemical $C _{1}, 50$ to chemical $C _{2},$ and $30$ to both the chemicals $C _{1}$ and $C _{2} .$ Find the number of individuals exposed to

Chemical $C_{1}$ or chemical $C_{2}$