Question

Out of $64$ students, the number of students taking Mathematics is $45$ and the number of students taking both Mathematics and Biology is $10$. Then, the number of students taking the only Biology is:

• A. $18$
• B. $19$
• C. $20$
• D. None of these

Answer 1

The correct option is B

$19$

Explanation for correct option

To find the number of students choosing biology:

Let $M$ denote the subject Mathematics and $B$ denote the subject Biology.

Number of students who took maths is denoted by $n\left(M\right)=45$

Number of students who took both mathematics and biology is denoted by$n(M\cap B)=10$

The total number of students is denoted by $n(M\cup B)=64$

Now, the number of students who took biology is given by:

$$\begin{gathered} n\left(B\right)=n(M\cup B)-n\left(M\right)+n(M\cap B) \\ =65-45+10 \\ =29 \end{gathered}$$

Further, the students taking only biology and not mathematics is given by:

$$\begin{gathered} n\left(B\right)=n\left(B\right)-n(M\cap B) \\ =29-10 \\ =19 \end{gathered}$$

Hence, the correct answer is Option B.