Question

In a survey of $300$ android mobile users, who make video calls, $75$ people said they use only viber, $45$ use only skype and $90$ people use both. The number of people who use neither viber nor skype is

• A. $40$
• B. $60$
• C. $80$
• D. $90$

Answer 1

The correct option is D $90$

Let $U$ denote the set of surveyed mobile users. $V$ denote set of people using Viber and $S$ denote set of people using Skype. Then, $n\left(U\right)=300,n(V\cap S)=90$
Number of persons using Viber = Number of persons using only Viber + Number of persons using both Viber and Skype
Therefore, $n\left(V\right)=75+90=165$
Number of persons using Skype = Number of persons using only Skype + Number of persons using both Viber and Skype
Therefore, $n\left(S\right)=45+90=135$

Now, no. of persons who use neither viber nor skype is given as,
$n\left(VUS\right)=n\left(V\right)+n\left(S\right)-n(V\cap S)$
$n\left(VUS\right)=165+135-90$
$n\left(VUS\right)=210$
$n(VUS{)}^{\prime }=n(U)-n(VUS)$
$n\left(VUS\right)=300-210$
$n\left(VUS\right)=90$