GATE ECE 2023 | GA Question: 4

Question

In a class of $100$ students,

1. there are $30$ students who neither like romantic movies nor comedy movies,
2. the number of students who like romantic movies is twice the number of students who like comedy movies, and
3. the number of students who like both romantic movies and comedy movies is $20$.

How many students in the class like romantic movies?

• A. $40$
• B. $20$
• C. $60$
• D. $30$

Answer 1

Given that:

• Total number of students in the class $=100$
• Number of students who neither like romantic movies nor comedy movies $=30$
• Number of students who like both romantic movies and comedy movies $=20$

Let’s draw the Venn diagram.

We can write,

• $n(U) = 100$
• $n\overline{(RM \cup CM)} = 30$
• $n(RM \cap CM) = 20$
• $n(RM) = n(2CM)$
• $n(RM \cup CM) = n(U) \;– \;n\overline{(RM \cup CM)}  = 100-30 = 70$

We know that$,n(RM \cup CM) = n(RM) + n(CM) – n(RM \cap CM)$

$\Rightarrow  70 = n(RM) + n(CM)-20$

$\Rightarrow n(RM) + n(CM) = 90$

$\Rightarrow n(2CM)  + n(CM) = 90$

$\Rightarrow n(3CM) = 90$

$\Rightarrow n(CM) = 30$

$\Rightarrow n(RM) = 60$

Therefore, there are $60$ students in the class who like romantic movies.