Sometimes ago in a Cinema hall a blockbuster movie was being shown. Due to excessive demand of the show, manager of the cinema hall increased the prices of tickets in all the three categories. `25%` in first class, `12.5%` in special class and `40%` in balcony. If the collection of one show was ₹ 218925, then find the collection from the balcony only given that the ratio of price of ticket (increased price) for first class, special class and balcony is 5: 9: 14 :

Options

A. 109462.5
B. 58800
C. 14400
D. Data insufficient

Answer

To solve the problem, we need to find the collection from the balcony given the total collection and the ratio of ticket prices after the increase. Let's break it down step by step.

### Step 1: Understand the Ratio of Ticket Prices
The ratio of the increased prices of tickets for first class, special class, and balcony is given as:
- First Class : Special Class : Balcony = 5 : 9 : 14

### Step 2: Assign Variables to Ticket Prices
Let the increased price of the tickets be:
- First Class = 5x
- Special Class = 9x
- Balcony = 14x

### Step 3: Calculate the Total Ratio
The total ratio is the sum of the parts:
Total ratio = 5 + 9 + 14 = 28

### Step 4: Calculate the Total Collection
The total collection from all categories is given as ₹218,925. This collection can be expressed in terms of the ratio:
Total Collection = (Total Ratio) * (Number of Tickets Sold) * (Price per Ticket)

However, since we do not have the number of tickets sold, we will focus on the proportions.

### Step 5: Find the Collection from Each Class
The collection from each class can be calculated based on the ratio of ticket prices:
- Collection from First Class = (5/28) * 218925
- Collection from Special Class = (9/28) * 218925
- Collection from Balcony = (14/28) * 218925

### Step 6: Calculate the Collection from the Balcony
Now, we can calculate the collection from the balcony:
Collection from Balcony = (14/28) * 218925
= (1/2) * 218925
= 109462.5

### Step 7: Final Result
The collection from the balcony is ₹109,462.50.