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.
The number of students (both male and female) who like all the given types of movies is approximately what per cent of the number of female student who like only one of the given type of movies?

Options

A. 12
B. 18
C. 32
D. 22

Answer

To solve the problem step by step, we will analyze the information provided and calculate the required values systematically.

### Step 1: Determine the number of male and female students
Given the ratio of male to female students is 9:7, we can express the number of male and female students in terms of a variable \( x \):
- Male students = \( 9x \)
- Female students = \( 7x \)

### Step 2: Calculate the total number of male students
From the problem, we know that:
- The total number of male students is \( 900x \) (as derived from the percentages).
- Therefore, \( 9x = 900x \) implies \( x = 100 \).

So:
- Male students = \( 9 \times 100 = 900 \)
- Female students = \( 7 \times 100 = 700 \)

### Step 3: Calculate the number of male students liking each type of movie
Using the percentages given for male students:
- Only Hollywood: \( 16\% \) of \( 900 = 0.16 \times 900 = 144 \)
- Only Bollywood: \( 22\% \) of \( 900 = 0.22 \times 900 = 198 \)
- Only Regional: \( 12\% \) of \( 900 = 0.12 \times 900 = 108 \)
- Only Hollywood and Bollywood: \( 30\% \) of \( 900 = 0.30 \times 900 = 270 \)
- Only Bollywood and Regional: \( 10\% \) of \( 900 = 0.10 \times 900 = 90 \)
- Only Regional and Hollywood: \( 6\% \) of \( 900 = 0.06 \times 900 = 54 \)
- Remaining male students liking all types of movies = 18

### Step 4: Calculate the total percentage accounted for male students
Adding the percentages:
\[ 16 + 22 + 12 + 30 + 10 + 6 + 4 = 100\% \]
Thus, the total accounted for is \( 96\% \) and the remaining \( 4\% \) corresponds to the students who like all three types of movies.

### Step 5: Calculate the number of female students liking each type of movie
Using the percentages given for female students:
- Only Hollywood: \( 14\% \) of \( 700 = 0.14 \times 700 = 98 \)
- Only Bollywood: \( 20\% \) of \( 700 = 0.20 \times 700 = 140 \)
- Only Regional: \( 8\% \) of \( 700 = 0.08 \times 700 = 56 \)
- Only Hollywood and Bollywood: \( 26\% \) of \( 700 = 0.26 \times 700 = 182 \)
- Only Bollywood and Regional: \( 18\% \) of \( 700 = 0.18 \times 700 = 126 \)
- Only Regional and Hollywood: \( 10\% \) of \( 700 = 0.10 \times 700 = 70 \)
- Remaining female students liking all types of movies = 14

### Step 6: Calculate the total number of female students liking only one type of movie
Adding the female students who like only one type of movie:
\[ 98 + 140 + 56 = 294 \]

### Step 7: Calculate the total number of students (both male and female) who like all types of movies
Total students who like all types of movies:
\[ 18 \text{ (male)} + 14 \text{ (female)} = 32 \]

### Step 8: Calculate the required percentage
Now, we need to find what percentage \( 32 \) is of \( 294 \):
\[ \text{Percentage} = \left( \frac{32}{294} \right) \times 100 \approx 10.87\% \]

### Final Answer
The number of students (both male and female) who like all the given types of movies is approximately \( 10.87\% \) of the number of female students who like only one of the given types of movies.