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,

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