Question

In a class of $175$ students, the following data shows the number of students opting one or more subjects. Mathematics $100$; Physics $70$; Chemistry $40$; Mathematics and Chemistry $28$; Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered mathematics alone?

• A. $35$
• B. $48$
• C. $60$
• D. $22$

Answer 1

The correct option is C $60$

$M$-Mathematics

$P$-Physics

$C$-Chemistry

Let $n(M\cap P-C)=x$ refer the venn diagram

Given $n(M\cup P\cup C)=147$

$n\left(M\right)=100,n\left(P\right)=70,n\left(C\right)=40$

$n(M\cap P)=28,n(M\cap P)=18+x,n(P\cap C)=23,n(M\cap P\cap C)=18$

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

$147=100+70+40-28-23-(18+x)+18$

$147=210-51-x$

$\Rightarrow 147=159-x$

$\Rightarrow x=12$

Hence, the number of students offered mathematics alone are $72-x$ which is $60.$