Question

In a survey of 60 people, it was found that 25 people read newspaper $H$, 26 read newspaper $T, 26$ read newspaper $I, 9$ read $H$ and $I, 11$ read $H$ and T, 8 read $T$ and $I, 3$ read all three newspapers.
The number of people who read exactly one newspaper, is

• A. 30
• B. 18
• C. 24
• D. 22

Answer 1

Answer: (A)

From above solution,

$ n(H \cup T \cup I)=52 $
$a+b+c+d+e+f+g=52 ....$(i)
$ n(H \cap I)=9 $
$ \Rightarrow b+e=9 ....$(ii)
$ n(H \cap T)=11 $
$ \Rightarrow f+e=11 .....$(iii)
$ n(T \cap I)=8$
$ \Rightarrow e+d=8.....$(iv)
$ n(H \cap T \cap I)=3 $
$ e=3 $
Adding Eqs. (ii), (iii) and (iv) and then subtracting from Eq. (i), we get
$a+c+g-2 e=24$
$a+c+g-6=24$
$a+c+g=30$
$\therefore$ Number of people who read exactly one newspaper, is 30 .