The following data refers to number of movies released in years 2001, 2003 and 2005.
Note:
(i) Total number of movies released = number of international movies + number of Indian movies
(ii) Total number of Indian movies released=Number of Bollywood movies + Number of regional "language movies.
24% of total number of movies released in 2001, are international movies. In 2003, total number of movies released was 900 more than that released in 2001, out of which 432 are international movies. In 2005, total number of movies released was twice of that released in 2001, out of which 20% are international movies. Out of Indian movies released in 2001, 2003 and 2005, regional language movies released are 40%, 25% and 25% respectively. Number of regional language movies released in 2005 is 600.
What is the avearge number of Indian movies released in all the given years?

Options

A. 1836
B. 1863
C. 1463
D. 1436

Answer

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

### Step 1: Define Variables
Let the total number of movies released in 2001 be \( X \).

### Step 2: Calculate International Movies in 2001
According to the problem, 24% of the total movies released in 2001 are international movies:
\[ \text{International movies in 2001} = 0.24X \]

### Step 3: Calculate Total Movies in 2003
The total number of movies released in 2003 is 900 more than that released in 2001:
\[ \text{Total movies in 2003} = X + 900 \]
Out of these, 432 are international movies.

### Step 4: Calculate Indian Movies in 2003
The number of Indian movies released in 2003 can be calculated as:
\[ \text{Indian movies in 2003} = (X + 900) - 432 = X + 468 \]

### Step 5: Calculate Total Movies in 2005
The total number of movies released in 2005 is twice that released in 2001:
\[ \text{Total movies in 2005} = 2X \]
Out of these, 20% are international movies:
\[ \text{International movies in 2005} = 0.20(2X) = 0.4X \]

### Step 6: Calculate Indian Movies in 2005
The number of Indian movies released in 2005 can be calculated as:
\[ \text{Indian movies in 2005} = 2X - 0.4X = 1.6X \]

### Step 7: Calculate Regional Language Movies
From the problem, we know that:
- In 2001, regional language movies are 40% of Indian movies.
- In 2003, regional language movies are 25% of Indian movies.
- In 2005, regional language movies are 25% of Indian movies.

We also know that the number of regional language movies released in 2005 is 600. Therefore:
\[ 0.25 \times (1.6X) = 600 \]
Solving for \( X \):
\[ 0.4X = 600 \quad \Rightarrow \quad X = \frac{600}{0.4} = 1500 \]

### Step 8: Calculate Total Movies in Each Year
Now we can calculate the total movies for each year:
- **2001**: \( X = 1500 \)
- **2003**: \( 1500 + 900 = 2400 \)
- **2005**: \( 2 \times 1500 = 3000 \)

### Step 9: Calculate Indian Movies in Each Year
Now we can calculate the Indian movies for each year:
- **2001**:
\[ \text{Indian movies in 2001} = 1500 - 0.24 \times 1500 = 1500 - 360 = 1140 \]
- **2003**:
\[ \text{Indian movies in 2003} = 2400 - 432 = 1968 \]
- **2005**:
\[ \text{Indian movies in 2005} = 3000 - 0.4 \times 1500 = 3000 - 600 = 2400 \]

### Step 10: Calculate Average Number of Indian Movies
Finally, we calculate the average number of Indian movies released over the three years:
\[ \text{Average} = \frac{1140 + 1968 + 2400}{3} = \frac{5508}{3} = 1836 \]

### Final Answer
The average number of Indian movies released in all the given years is **1836**.

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