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 total number of Bollywood movies released in years 2001 and 2003 together?

Options

A. 2400
B. 2180
C. 2160
D. 2140

Answer

To solve the problem step by step, we will analyze the information given and derive the necessary values.

### Step 1: Define Variables
Let:
- \( A \) = Total number of movies released in 2001
- \( B \) = Total number of movies released in 2003
- \( C \) = Total number of movies released in 2005

### Step 2: Find Total Movies Released in 2001
According to the problem, 24% of total movies released in 2001 are international movies. Therefore, we can express this as:
\[ \text{International movies in 2001} = 0.24A \]
Thus, the total number of Indian movies in 2001 is:
\[ \text{Indian movies in 2001} = A - 0.24A = 0.76A \]

### Step 3: Find Total Movies Released in 2003
It is given that the total number of movies released in 2003 is 900 more than that released in 2001:
\[ B = A + 900 \]
Out of these, 432 are international movies. Therefore, the number of Indian movies in 2003 is:
\[ \text{Indian movies in 2003} = B - 432 = (A + 900) - 432 = A + 468 \]

### Step 4: Find Total Movies Released in 2005
It is stated that the total number of movies released in 2005 is twice that released in 2001:
\[ C = 2A \]
Out of these, 20% are international movies:
\[ \text{International movies in 2005} = 0.20C = 0.20(2A) = 0.40A \]
Thus, the number of Indian movies in 2005 is:
\[ \text{Indian movies in 2005} = C - 0.40A = 2A - 0.40A = 1.60A \]

### Step 5: Find Regional Language Movies
The problem states that the percentage of regional language movies among Indian movies is as follows:
- In 2001: 40%
- In 2003: 25%
- In 2005: 25%

From the data, we know that the number of regional language movies released in 2005 is 600. Therefore:
\[ 0.25 \times \text{Indian movies in 2005} = 600 \]
\[ 0.25 \times 1.60A = 600 \]
\[ 0.40A = 600 \]
\[ A = \frac{600}{0.40} = 1500 \]

### Step 6: Calculate Total Movies Released in Each Year
Now that we have \( A \):
- Total movies in 2001: \( A = 1500 \)
- Total movies in 2003: \( B = 1500 + 900 = 2400 \)
- Total movies in 2005: \( C = 2 \times 1500 = 3000 \)

### Step 7: Calculate Indian Movies in Each Year
- Indian movies in 2001:
\[ 0.76A = 0.76 \times 1500 = 1140 \]
- Indian movies in 2003:
\[ B - 432 = 2400 - 432 = 1968 \]
- Indian movies in 2005:
\[ 1.60A = 1.60 \times 1500 = 2400 \]

### Step 8: Calculate Bollywood Movies
Now we calculate the number of Bollywood movies:
- Bollywood movies in 2001 (60% of Indian movies):
\[ 0.60 \times 1140 = 684 \]
- Bollywood movies in 2003 (75% of Indian movies):
\[ 0.75 \times 1968 = 1476 \]

### Step 9: Total Bollywood Movies Released in 2001 and 2003
Finally, we sum the Bollywood movies from 2001 and 2003:
\[ \text{Total Bollywood movies} = 684 + 1476 = 2160 \]

### Answer
The total number of Bollywood movies released in years 2001 and 2003 together is **2160**.

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