You are shown a set of statements below. You have to use the data in these statements to find the answer to the fill in the blank question on your right. Not all the data may be relevant or needed. Round decimal answers to the next whole number. is the number of movie halls in Delhi 1) Total population of Delhi is 22 million. 2) Total average monthly revenue per hall is Rs.1.2 billion. 3) The average price of the ticket is Rs. 200. 4) On any particular day, 10 movies are running in Cinema halls. 5) Around 30% of the population is below 14 years of age. 6) Around 5% of the population is above 60 years of age. 7) 5% children below 14 years of age and 5% of people above 60 years of age go for an average one movie per month. usty 8) 20% of total population in age group 14-60 years go for an average 2 movies per month. 9) 80% of the halls are multiplexes (4 screens) and 20% are single screen movie halls. 10) Average optimum capacity per screen: 300 cinema goers. 11) Monday to Friday, average occupancy is 40% and on Saturday- Sunday, average occupancy goes up to 70%. 12) There are on an average 4 shows per screen per day.

To find the number of movie halls in Delhi, we will first determine the number of people going to movies and then use that to estimate the number of movie halls needed to accommodate them.

### Step 1: Calculate the number of people going to movies
The population of Delhi is 22 million.

#### People below 14 years:
- 30% of 22 million are below 14 years:  
  \( 0.30 \times 22 \) million = 6.6 million.
- 5% of children below 14 years go to an average of 1 movie per month:  
  \( 0.05 \times 6.6 \) million = 0.33 million moviegoers per month.

#### People above 60 years:
- 5% of 22 million are above 60 years:  
  \( 0.05 \times 22 \) million = 1.1 million.
- 5% of people above 60 years go to an average of 1 movie per month:  
  \( 0.05 \times 1.1 \) million = 0.055 million moviegoers per month.

#### People aged 14-60 years:
- The remaining 65% of the population are between 14-60 years:  
  \( 0.65 \times 22 \) million = 14.3 million.
- 20% of this group go to an average of 2 movies per month:  
  \( 0.20 \times 14.3 \) million = 2.86 million people.  
  They watch 2 movies per month, so total moviegoers per month from this group:  
  \( 2.86 \times 2 = 5.72 \) million.

### Total monthly moviegoers
Adding the monthly moviegoers from all age groups:  
\( 0.33 + 0.055 + 5.72 = 6.105 \) million moviegoers per month.

### Step 2: Calculate the total number of shows per month
There are 4 shows per screen per day and 30 days in a month:  
Total shows per screen per month: \( 4 \times 30 = 120 \) shows.

### Step 3: Calculate the average daily occupancy rate
- Average occupancy on weekdays (5 days): 40%
- Average occupancy on weekends (2 days): 70%
  
Weekly average occupancy = \(\frac{(5 \times 0.40) + (2 \times 0.70)}{7} = \frac{2 + 1.4}{7} = 0.4857 \approx 48.57\% \).

### Step 4: Calculate the number of screens required
- Optimum capacity per screen = 300 cinema-goers
- Adjusted occupancy capacity per screen per show = \( 0.4857 \times 300 = 145.71 \) people per show.

Total monthly capacity per screen:  
\( 145.71 \times 120 \) = 17,485.2 people per screen per month.

### Step 5: Calculate the number of screens required
Total number of screens needed:  
\( \frac{6.105 \text{ million}}{17,485.2} = \frac{6,105,000}{17,485.2} \approx 349.15 \) screens.

### Step 6: Calculate the number of movie halls
- 80% of the halls are multiplexes with 4 screens each.
- 20% of the halls are single-screen movie halls.

Let \( x \) be the total number of halls.
\[ 0.8x \times 4 + 0.2x \times 1 = 349.15 \]
\[ 3.2x + 0.2x = 349.15 \]
\[ 3.4x = 349.15 \]
\[ x = \frac{349.15}{3.4} \approx 102.7 \]

Rounding to the nearest whole number, the total number of movie halls in Delhi is **103**.

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**Summary:** The number of movie halls in Delhi is approximately **103**. 

Do you want more details or have any questions?

Here are some related questions:
1. How would the number of movie halls change if the population increased by 10%?
2. What impact does the occupancy rate have on the required number of movie halls?
3. How would the number of required movie halls change if the average price of the ticket increased?
4. What would happen if only 60% of the moviegoers aged 14-60 years watched movies?
5. How would reducing the number of shows per day affect the number of movie halls required?

**Tip:** When solving problems involving multiple data points, break the problem into smaller parts and solve each step methodically.

Learn how to calculate the number of movie halls in Delhi based on population size, average monthly revenue per hall, ticket prices, and moviegoing habits. This problem involves arithmetic calculations, statistics, and probability concepts. Suitable for high school students and beyond.

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