Question

In a class of $345$ students, the students who took English, Math and Physics are equal in number. $30$ students took English and Math, $26$ choose Math and Physics, $28$ choose Physics and English and $14$ choose all three subjects. $43$ students didn’t take any of the subjects. How many students have taken English as subject?

• A. $108$
• B. $124$
• C. $246$
• D. $286$

Answer 1

The correct option is B $124$

Let $x$ no. of students chooses English
$\therefore n\left(E\right)=n\left(M\right)=n\left(P\right)=x$
$\therefore n(E\cup M\cup P)=n\left(E\right)+n\left(M\right)+n\left(P\right)-n(E\cap M)-n(M\cap P)-n(P\cap E)+n(E\cap M\cap P)$
$\Rightarrow 302=3x-84+14$
$\Rightarrow x=124$