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 difference between the number of male student who like Bollywood movies and the number of female students who like the same ?

Options

A. 69
B. 59
C. 63
D. 65

Answer

To solve the problem, we need to find the difference between the number of male students who like Bollywood movies and the number of female students who like Bollywood movies based on the given percentages. Let's break it down step by step.

### Step 1: Define the Variables
Let the total number of male students be \( 900x \) and the total number of female students be \( 700x \) based on the ratio of male to female students (9:7).

### Step 2: Calculate Male Students Preferences
1. **Only Hollywood Movies**:
\[ 16\% \text{ of } 900x = \frac{16}{100} \times 900x = 144x \]

2. **Only Bollywood Movies**:
\[ 22\% \text{ of } 900x = \frac{22}{100} \times 900x = 198x \]

3. **Only Regional Movies**:
\[ 12\% \text{ of } 900x = \frac{12}{100} \times 900x = 108x \]

4. **Only Hollywood and Bollywood**:
\[ 30\% \text{ of } 900x = \frac{30}{100} \times 900x = 270x \]

5. **Only Bollywood and Regional**:
\[ 10\% \text{ of } 900x = \frac{10}{100} \times 900x = 90x \]

6. **Only Regional and Hollywood**:
\[ 6\% \text{ of } 900x = \frac{6}{100} \times 900x = 54x \]

7. **All Three Types of Movies**:
Given that 18 male students like all three types.

### Step 3: Total Male Students Calculation
Now, we can set up the equation for the total male students:
\[ 144x + 198x + 108x + 270x + 90x + 54x + 18 = 900x \]
Calculating the left side:
\[ 144x + 198x + 108x + 270x + 90x + 54x + 18 = 862x + 18 \]
Setting it equal to the total number of male students:
\[ 862x + 18 = 900x \]
Solving for \( x \):
\[ 900x - 862x = 18 \implies 38x = 18 \implies x = \frac{18}{38} = \frac{9}{19} \]

### Step 4: Total Male Students
Substituting \( x \) back:
\[ \text{Total Male Students} = 900x = 900 \times \frac{9}{19} = 425.26 \approx 450 \text{ (rounding for practical purposes)} \]

### Step 5: Calculate Female Students Preferences
1. **Only Hollywood Movies**:
\[ 14\% \text{ of } 700x = \frac{14}{100} \times 700x = 98x \]

2. **Only Bollywood Movies**:
\[ 20\% \text{ of } 700x = \frac{20}{100} \times 700x = 140x \]

3. **Only Regional Movies**:
\[ 8\% \text{ of } 700x = \frac{8}{100} \times 700x = 56x \]

4. **Only Hollywood and Bollywood**:
\[ 26\% \text{ of } 700x = \frac{26}{100} \times 700x = 182x \]

5. **Only Bollywood and Regional**:
\[ 18\% \text{ of } 700x = \frac{18}{100} \times 700x = 126x \]

6. **Only Regional and Hollywood**:
\[ 10\% \text{ of } 700x = \frac{10}{100} \times 700x = 70x \]

7. **All Three Types of Movies**:
Remaining female students like all three types.

### Step 6: Total Female Students Calculation
Setting up the equation for total female students:
\[ 98x + 140x + 56x + 182x + 126x + 70x + 14 = 700x \]
Calculating the left side:
\[ 98x + 140x + 56x + 182x + 126x + 70x + 14 = 672x + 14 \]
Setting it equal to the total number of female students:
\[ 672x + 14 = 700x \]
Solving for \( x \):
\[ 700x - 672x = 14 \implies 28x = 14 \implies x = \frac{14}{28} = \frac{1}{2} \]

### Step 7: Total Female Students
Substituting \( x \) back:
\[ \text{Total Female Students} = 700x = 700 \times \frac{1}{2} = 350 \]

### Step 8: Calculate Bollywood Preferences
1. **Male Students who like Bollywood**:
\[ 198x + 270x + 90x + 18 = 198 \times \frac{9}{19} + 270 \times \frac{9}{19} + 90 \times \frac{9}{19} + 18 \]
Simplifying gives:
\[ 198 + 270 + 90 + 18 = 576x \approx 576 \times \frac{9}{19} = 273.68 \approx 274 \]

2. **Female Students who like Bollywood**:
\[ 140x + 182x + 126x + 14 = 140 \times \frac{1}{2} + 182 \times \frac{1}{2} + 126 \times \frac{1}{2} + 14 \]
Simplifying gives:
\[ 140 + 182 + 126 + 14 = 462x \approx 462 \times \frac{1}{2} = 231 \]

### Step 9: Calculate the Difference
Finally, we find the difference:
\[ \text{Difference} = 274 - 231 = 43 \]

### Conclusion
The difference between the number of male students who like Bollywood movies and the number of female students who like the same is **43**.