Question

In a class of 55 students, the number of students studying different subjects are 23 in Mathematics and 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects, The number of students who have taken exactly one subject is

• A. 20
• B. 24
• C. 23
• D. 22

Answer 1

The correct option is D 22

Total no. of student=55

Let n(M)=student who studying mathematics

n(C)=student who studying chemistry

n(P)=student who studying Physics

$\therefore n\left(M\right)=23,n\left(P\right)=24,n\left(C\right)=19,n(M\cap P)=12,n(M\cap C)=9,n(P\cap C)=7,n(M\cap P\cap C)=4$

Number of student who studying mathematics but not physic and chemistry

$\Rightarrow n\left(M\right)-\left[\right(n(M\cap C)+n(M\cap P)]+n(M\cap P\cap C)$

$\Rightarrow 23-[9+12]+4$

$\Rightarrow 23-21+4=6$

Number of student who studying chemistry but not physic and matehematics

$\Rightarrow n\left(C\right)-\left[\right(n(M\cap C)+n(P\cap C)]+n(M\cap P\cap C)$

$\Rightarrow 19-[9+7]+4$

$\Rightarrow 19-16+4=7$

Number of student who studying physics but not mathematics and chemistry

$\Rightarrow n\left(P\right)-\left[\right(n(M\cap P)+n(P\cap C)]+n(M\cap P\cap C)$

$\Rightarrow 24-[12+7]+4$

$\Rightarrow 24-19+4=9$

$\therefore$no. of student studying exactly one subject$=6+7+9=22$