Read the information given in the passage and answer the given question.
There are ‘X’ number of student in a college. Each of them likes either one or more of the following types of movies – Hollywood, Bollywood and Regional. The ratio of male to female student is 9:7. `16%` of the male student like only Hollywood movies. `22%` like only Bollywood movies . `12%` like only Regional movies `30%` of the male students like only Hollywood and Bollywood movies. `10%` like only Bollywood and Regional movies and `6%` like only Regional and Hollywood movies. The remaining 18 male students like all the given type of movies.
`14%` of the female students like only Hollywood movies. `20%` like only Bollywood movies. `8%` like only Regional movies. `26%` of the female students like only Hollywood and Bollywood movies. `18%` like only Bollywood and Regional movies and `10%` like only Regional and Hollywood movies. The remaining female students like all the given type of movies.
What is the value of ‘X’ (mentioned in the passage)?

Options

A. 960
B. 800
C. 640
D. 720

Answer

To find the total number of students \(X\) in the college, we will follow these steps:

### Step 1: Define the ratio of male to female students
The ratio of male to female students is given as \(9:7\). This means for every 9 male students, there are 7 female students.

Let the number of male students be \(9k\) and the number of female students be \(7k\), where \(k\) is a common multiplier.

### Step 2: Calculate the total number of male students
We know the percentages of male students who like different types of movies:
- Only Hollywood: \(16\%\)
- Only Bollywood: \(22\%\)
- Only Regional: \(12\%\)
- Only Hollywood and Bollywood: \(30\%\)
- Only Bollywood and Regional: \(10\%\)
- Only Regional and Hollywood: \(6\%\)
- All three types of movies: \(18\) students

First, we calculate the total percentage of male students accounted for:
\[ 16 + 22 + 12 + 30 + 10 + 6 = 96\% \]
This means \(4\%\) of the male students like all three types of movies.

### Step 3: Set up the equation for male students
Since \(4\%\) of male students equals \(18\) students, we can set up the equation:
\[ 0.04 \times (9k) = 18 \]
Solving for \(k\):
\[ 9k = \frac{18}{0.04} = 450 \]
\[ k = \frac{450}{9} = 50 \]

### Step 4: Calculate the number of male students
Now we can find the number of male students:
\[ \text{Number of male students} = 9k = 9 \times 50 = 450 \]

### Step 5: Calculate the number of female students
Using the value of \(k\):
\[ \text{Number of female students} = 7k = 7 \times 50 = 350 \]

### Step 6: Calculate the total number of students
Now we can find the total number of students \(X\):
\[ X = \text{Number of male students} + \text{Number of female students} = 450 + 350 = 800 \]

Thus, the value of \(X\) is \(800\).