Question

In a class of $100$ students, $55$ students have passed in Mathematics and $67$ students have passed in physics. Then the number of students who have passed in physics only is

• A. $22$
• B. $33$
• C. $10$
• D. $45$

Answer 1

The correct option is D $45$

The number of students passed in Mathematics, $n\left(M\right)=55$

The number of students passed in Physics, $n\left(P\right)=67$

Total number of students, $n(M\cup P)=100$

Let no. of students passed in both subjects $=n(P\cap M)$

$n(M\cup P)=n\left(M\right)+n\left(P\right)-n(P\cap M)$

$100=55+67-n(P\cap M)$

$n(P\cap M)=122-100=22$

No. of students passed in Physics but not in Maths, $n(P\cap M^{\prime })=n\left(P\right)-n(P\cap M)$

$=67-22$

$=45$