Question

In a class of 175 students the following data shows the number of students 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. How many students have offered Mathematics alone ?

• A. 35
• B. 48
• C. 60
• D. 22

Answer 1

The correct option is C

60

Let M be the set of students who study mathematics, P be the set of students who study physics and C be the set of students who study chemistry.

Then, n(U) = 175, n(M)= 100, n(P)= 70 and n(C) = 40

$n(M\cap P)=30,n(M\cap C)=28andn(P\cap C)=23$

$n(M\cap P\cap C)=18$

$\because n\left(M\right)=100$

$\Rightarrow a+b+e+f=100$ ....(i)

Now n(P) = 70

$\Rightarrow b+c+d+e=70$ ....(ii)

Now n(C) = 40

$\Rightarrow$ f+e+d+g = 40 ....(iii)

Now $n(M\cap P)$= 30

$\Rightarrow$ b+ e = 30 ....(iv)

Now $n(M\cap P)$ = 28

$\Rightarrow$ e +f = 28 ....(v)

Now $n(P\cap C)$= 23

$\Rightarrow$ d + e = 23 ....(vi)

Now $n(M\cap P\cap C)$= 18

$\Rightarrow$ e = 18 ....(vii)

from Equation (vi) and (vii), d = 5

from Equation (v) and (vii), f = 10

from Equation (iv) and (vii), b = 12

On substituting the value of b, e, f in equation (i) we get

$\Rightarrow a+b+e+f=100$

a+12+18+10= 100

a= 60 ....(c)