Question

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

• A. $20$
• B. $30$
• C. $40$
• D. $10$

Answer 1

The correct option is A $20$

$M\cup P\cup C$ $=n\left(M\right)+n\left(P\right)+n\left(C\right)-n(M\cap P+P\cap C+C\cap M)+n(M\cap P\cap C)$
Therefore,
$(200-20)=120+90+70-40-30-50+x$
$180=90+70+x$
$180-160=x$
$x=20$
$M\cap P\cap C=20$