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. $30$

Comments

similar question:
https://gateoverflow.in/422904/gate-cse-2024-set-2-ga-question-3

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.

Correct Answer :- Option C) 

Answer 2

You

Let's denote:

• R as the number of students who like romantic movies,
• C as the number of students who like comedy movies.

We know:

1. There are 30 students who neither like romantic nor comedy movies.
2. The number of students who like romantic movies is twice the number of students who like comedy movies, so R = 2C.
3. The number of students who like both romantic and comedy movies is 20.

We can set up an equation using the principle of inclusion-exclusion: Total students = R + C - (students who like both romantic and comedy movies) + (students who like neither romantic nor comedy movies).

Substituting the given values: 100 = R + C - 20 + 30.

Since R = 2C, we can substitute R with 2C in the equation: 100 = 2C + C - 20 + 30.

Now, solving for C: 100 = 3C + 10.

Subtracting 10 from both sides: 90 = 3C.

Dividing both sides by 3: C = 30.

Now, substituting the value of C back into R = 2C: R = 2 * 30, R = 60.

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

Answer 3

I got first 40 but they asked not only romantic so answer is 60

Answer 4

Ans:C 60