The entry ticket at a fun park was increased in the ratio `7:9`, due to which footfalls fell in the ratio `13: 11`. What is the new daily collection (in Rs.), if the daily collection before the price hike was `Rs. 2,27,500`?

Options

A. 237500
B. 247500
C. 232500
D. 242500

Answer

To solve the problem step-by-step, we need to analyze the ratios given for the ticket price increase and the decrease in footfalls, then calculate the new daily collection based on the old daily collection.

### Step 1: Understand the Ratios
The ticket price increased in the ratio of 7:9. This means if the old price is represented as 7 parts, the new price is represented as 9 parts.

The footfalls (number of visitors) decreased in the ratio of 13:11. This means if the old footfalls are represented as 13 parts, the new footfalls are represented as 11 parts.

### Step 2: Calculate the Old Price and New Price
Let’s denote the old ticket price as \( P \). The new ticket price can be calculated as follows:

- Old Price = 7 parts
- New Price = 9 parts

Thus, the new price in terms of the old price \( P \) is:
\[ \text{New Price} = \frac{9}{7} \times P \]

### Step 3: Calculate the Old Footfalls and New Footfalls
Let’s denote the old footfalls as \( F \). The new footfalls can be calculated as follows:

- Old Footfalls = 13 parts
- New Footfalls = 11 parts

Thus, the new footfalls in terms of the old footfalls \( F \) is:
\[ \text{New Footfalls} = \frac{11}{13} \times F \]

### Step 4: Calculate the Old Daily Collection
The old daily collection is given as Rs. 2,27,500. The daily collection can be expressed as:
\[ \text{Old Daily Collection} = \text{Old Price} \times \text{Old Footfalls} \]

### Step 5: Set Up the Equation for New Daily Collection
The new daily collection can be expressed as:
\[ \text{New Daily Collection} = \text{New Price} \times \text{New Footfalls} \]

Substituting the expressions for new price and new footfalls:
\[ \text{New Daily Collection} = \left(\frac{9}{7} \times P\right) \times \left(\frac{11}{13} \times F\right) \]

### Step 6: Relate New Daily Collection to Old Daily Collection
We can relate the new daily collection to the old daily collection:
\[ \text{New Daily Collection} = \frac{9}{7} \times \frac{11}{13} \times \text{Old Daily Collection} \]

### Step 7: Substitute the Old Daily Collection
Now we substitute the value of the old daily collection:
\[ \text{New Daily Collection} = \frac{9}{7} \times \frac{11}{13} \times 227500 \]

### Step 8: Calculate the New Daily Collection
Now, we calculate:
1. Calculate \( \frac{9 \times 11}{7 \times 13} \):
\[ \frac{99}{91} \]
2. Now, multiply this by the old daily collection:
\[ \text{New Daily Collection} = \frac{99}{91} \times 227500 \]

Calculating:
\[ \text{New Daily Collection} = 227500 \times \frac{99}{91} \]

Calculating \( 227500 \div 91 \):
\[ 227500 \div 91 = 2500 \]

Then multiply by 99:
\[ 2500 \times 99 = 247500 \]

### Final Answer
The new daily collection is Rs. 2,47,500.

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