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 male students who like only two of the given types of movies is what per cent more than the number of female student who like only two of the given types of movies?

Options

A. `11 1/21`
B. `16 1/7`
C. `9 11/21`
D. `8 1/7`

Answer

To solve the problem step-by-step, we will first summarize the information provided and then calculate the required values.

### Step 1: Define the Variables
Let the total number of male students be \( M \) and female students be \( F \). According to the problem, the ratio of male to female students is \( 9:7 \). We can express this as:
- \( M = 9x \)
- \( F = 7x \)

### Step 2: Calculate Male Students
From the problem, we know:
- \( 16\% \) of male students like only Hollywood movies: \( 0.16M = 0.16(9x) = 1.44x \)
- \( 22\% \) like only Bollywood movies: \( 0.22M = 0.22(9x) = 1.98x \)
- \( 12\% \) like only Regional movies: \( 0.12M = 0.12(9x) = 1.08x \)
- \( 30\% \) like only Hollywood and Bollywood: \( 0.30M = 0.30(9x) = 2.7x \)
- \( 10\% \) like only Bollywood and Regional: \( 0.10M = 0.10(9x) = 0.9x \)
- \( 6\% \) like only Regional and Hollywood: \( 0.06M = 0.06(9x) = 0.54x \)
- Remaining male students like all three types of movies: \( 18 \)

### Step 3: Calculate Total Percentage for Males
Now, we will sum the percentages of male students who like one or two types of movies:
\[ 16 + 22 + 12 + 30 + 10 + 6 = 96\% \]
This means \( 4\% \) of male students like all three types of movies. Thus, we can set up the equation:
\[ 0.04M = 18 \implies M = \frac{18}{0.04} = 450 \]
So, \( M = 450 \) and substituting back, we find \( x \):
\[ 9x = 450 \implies x = 50 \]
Thus, \( F = 7x = 350 \).

### Step 4: Calculate Female Students
Now we will calculate the number of female students who like different types of movies:
- \( 14\% \) like only Hollywood: \( 0.14F = 0.14(350) = 49 \)
- \( 20\% \) like only Bollywood: \( 0.20F = 0.20(350) = 70 \)
- \( 8\% \) like only Regional: \( 0.08F = 0.08(350) = 28 \)
- \( 26\% \) like only Hollywood and Bollywood: \( 0.26F = 0.26(350) = 91 \)
- \( 18\% \) like only Bollywood and Regional: \( 0.18F = 0.18(350) = 63 \)
- \( 10\% \) like only Regional and Hollywood: \( 0.10F = 0.10(350) = 35 \)
- Remaining female students like all three types of movies.

### Step 5: Calculate Total Percentage for Females
Now, we will sum the percentages of female students who like one or two types of movies:
\[ 14 + 20 + 8 + 26 + 18 + 10 = 96\% \]
This means \( 4\% \) of female students like all three types of movies:
\[ 0.04F = 0.04(350) = 14 \]

### Step 6: Calculate Male and Female Students Who Like Only Two Types of Movies
For males:
- Only Hollywood and Bollywood: \( 2.7x = 2.7(50) = 135 \)
- Only Bollywood and Regional: \( 0.9x = 0.9(50) = 45 \)
- Only Regional and Hollywood: \( 0.54x = 0.54(50) = 27 \)

Total males who like only two types of movies:
\[ 135 + 45 + 27 = 207 \]

For females:
- Only Hollywood and Bollywood: \( 91 \)
- Only Bollywood and Regional: \( 63 \)
- Only Regional and Hollywood: \( 35 \)

Total females who like only two types of movies:
\[ 91 + 63 + 35 = 189 \]

### Step 7: Calculate the Percentage Difference
Now we need to find out what percentage more the number of male students who like only two types of movies is compared to female students who like only two types of movies:
\[ \text{Difference} = 207 - 189 = 18 \]
\[ \text{Percentage more} = \left(\frac{18}{189}\right) \times 100 \approx 9.52\% \]

### Final Answer
The number of male students who like only two of the given types of movies is approximately **9.52%** more than the number of female students who like only two of the given types of movies.