Rubina could get equal number of Rs. 55 , Rs. 85 and Rs. 105 tickets for a movie. She spents Rs. 2,940 for all the tickets. How many of each did she buy ?

Options

A. 12
B. 14
C. 16
D. Can’t be determined

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let \( X \) be the number of tickets of each type that Rubina buys. Therefore, she buys \( X \) tickets of Rs. 55, \( X \) tickets of Rs. 85, and \( X \) tickets of Rs. 105.

### Step 2: Write the Equation
The total cost of the tickets can be expressed as:
\[ \text{Total Cost} = (\text{Number of Rs. 55 tickets} \times \text{Price of Rs. 55 ticket}) + (\text{Number of Rs. 85 tickets} \times \text{Price of Rs. 85 ticket}) + (\text{Number of Rs. 105 tickets} \times \text{Price of Rs. 105 ticket}) \]
Substituting the values, we get:
\[ 2940 = (55X) + (85X) + (105X) \]

### Step 3: Combine Like Terms
Now, we combine the terms on the right side:
\[ 2940 = 55X + 85X + 105X = (55 + 85 + 105)X = 245X \]

### Step 4: Solve for X
Now we can solve for \( X \):
\[ 245X = 2940 \]
To find \( X \), divide both sides by 245:
\[ X = \frac{2940}{245} \]

### Step 5: Calculate X
Now, we perform the division:
\[ X = 12 \]

### Conclusion
Rubina bought 12 tickets of each type (Rs. 55, Rs. 85, and Rs. 105).