In a cricket match there are three types of tickets say A B and C each costing Rs. 1000, Rs. 500 and Rs. 200 respectively. The ratio of the tickets sold of categories A B and C is `3 : 2 : 5`. If the total collection from selling the tickets Is Rs 2.5 crore, find the total number of tickets sold?

Options

A. 5000
B. 4800
C. 50000
D. 52000

Answer

To solve the problem, we need to determine the total number of tickets sold based on the given prices and the ratio of tickets sold.

### Step 1: Understand the ticket prices and the ratio
The prices of the tickets are:
- Ticket A: Rs. 1000
- Ticket B: Rs. 500
- Ticket C: Rs. 200

The ratio of tickets sold is:
- A : B : C = 3 : 2 : 5

### Step 2: Assign variables based on the ratio
Let the number of tickets sold for:
- A = 3x
- B = 2x
- C = 5x

### Step 3: Calculate the total revenue from ticket sales
The total revenue from selling the tickets can be calculated as follows:
- Revenue from A = 3x * 1000 = 3000x
- Revenue from B = 2x * 500 = 1000x
- Revenue from C = 5x * 200 = 1000x

Now, we can find the total revenue:
\[ \text{Total Revenue} = 3000x + 1000x + 1000x = 5000x \]

### Step 4: Set the total revenue equal to the given total collection
We know that the total collection from selling the tickets is Rs. 2.5 crore, which is Rs. 2,50,00,000.

So, we set up the equation:
\[ 5000x = 2,50,00,000 \]

### Step 5: Solve for x
To find x, we divide both sides of the equation by 5000:
\[ x = \frac{2,50,00,000}{5000} \]
\[ x = 50,000 \]

### Step 6: Calculate the total number of tickets sold
Now, we can find the total number of tickets sold:
\[ \text{Total Tickets} = 3x + 2x + 5x = 10x \]
Substituting the value of x:
\[ \text{Total Tickets} = 10 \times 50,000 = 5,00,000 \]

### Final Answer
The total number of tickets sold is **5,00,000**.

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