Question

In a class $100$ 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

• A. $22$
• B. $23$
• C. $10$
• D. $45$

Answer 1

The correct option is D

$45$

Explanation for correct option:

Find the number of students passed in physics.

Let, $P$ be the number of students who passed in physics and $M$ be the number of students who passed in maths.

Then,
Number of students who passed in physics$$\begin{gathered} =n\left(P\right) \\ =67 \end{gathered}$$
Number of students who passed in maths $$\begin{gathered} =n\left(M\right) \\ =55 \end{gathered}$$

Number of students who passed both physics and maths is given by $=n(P\cap M)$

We know, $\mathit{n}\mathbf{(}\mathit{P}\mathbf{\cup }\mathit{M}\mathbf{)}\mathbf{=}\mathit{n}\mathbf{\left(}\mathit{P}\mathbf{\right)}\mathbf{+}\mathit{n}\mathbf{\left(}\mathit{M}\mathbf{\right)}\mathbf{-}\mathit{n}\mathbf{(}\mathit{P}\mathbf{\cap }\mathit{M}\mathbf{)}$

Substituting the given values we get,

$$\begin{gathered} \Rightarrow 100=55+67-n(P\cap M) \\ \Rightarrow n(P\cap M)=122-100 \\ \Rightarrow n(P\cap M)=22 \end{gathered}$$

Now, number of students who passed only in physics,

$=$Number of students passed in physics $-$ Number of students passed in both physics and maths

$$\begin{gathered} =67-22 \\ =45 \end{gathered}$$

Hence, the correct option is D.