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 Physics $30$; Mathematics and Chemistry $28$; Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$.
Then, number of students opted Mathematics alone is

• A. 35
• B. 48
• C. 60
• D. 20

Answer 1

Answer: (C)

Given, $n(M)=100,n(P)=70,n(C)=40$
$n(M\cap P)=30,n(M\cap C)=28$
$n(P\cap C)=23$
and $n(M\cap P\cap C)=18$
$\therefore n\left(M\cap P^{\prime }\cap C^{\prime }\right)=n\left[M\cap (P\cup C{)}^{\gamma }\right]$
$=n(M)-n[M\cap (P\cup C)]$
$\left[\because n\left(A\cap B^{\prime }\right)=n(A)-n(B)\right]$
$=n(M)-n[(M\cap P)\cup (M\cap C)]$
$=n(M)-[n(M\cap P)+n(M\cap C)$
$-n(M\cap P\cap C)]$
$=100-[30+28-18]$
$=100-40$
$=60$