Question

Ina city 65% of the people view Tamil movies and 40% view English movies, 20$ of the people view both Tamil and English movies. Find the percentage of people do not view any of these two movies.

Answer 1

Let the population o the city be 100. Let $T$ denote the set of people who view Tamil movies and $E$ denote the set of people who view English movies. Then $n\left(T\right)=65,n\left(E\right)=40,n(T\cap E)=20$. So, the number of people who view either of these movies is
$n(T\cup E)=n\left(T\right)+n\left(E\right)-n(T\cap E)$
$=65+40-20=85$
Hence the number of people who do not view any of these movies is $100-85=15$
Hence the percentage of people who do not view any of these movies is 15
Aliter
From the Venn diagram the percentage of people who view at least one of these two movies is
$45+20+20=85$
Hence the percentage of people who do not view any of these movies $=100-85=15$