In a battle $70\%$ of the combatants lost one eye, $80\%$ an ear, $75\%$ an arm, $85\%$ a leg, $x\%$ lost all the four limbs. The minimum value of $x$ is

A group of $40$ students appeared in an examination of $3$ subjects - Mathematics, Physics  Chemistry. It was found that all students passed in at least one of the subjects, $20$ students passed in Mathematics, $25$ students passed in Physics, $16$ students passed in Chemistry, at most $11$ students passed in both Mathematics and Physics, at most $15$ students passed in both Physics and Chemistry, at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is___________.

In a survey of $600$ students in a school, $150$ students were found to be taking tea and $225$ taking coffee, $100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

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 $C _{1}$ but not chemical $C _{2}$

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 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