The price of a movie ticket is increased in the ratio 9:10 while the number of tickets sold remains 2,200. If the original ticket fare was Rs. 180, what is the increase in the cinema hall's total revenue (in Rs.)?

Introduction / Context:
This problem is a direct application of percentage or ratio based increase in revenue. Whenever price changes and quantity remains the same, the new revenue can be found very quickly by scaling the old revenue by the corresponding ratio. Here we are told exactly how the ticket price changes and how many tickets are sold, which makes the calculation straightforward.

Given Data / Assumptions:

Original movie ticket price = Rs. 180 per ticket.
Number of tickets sold = 2,200 and this quantity does not change.
Ticket price is increased in the ratio 9:10 (old price : new price).
We need the increase in total revenue in rupees, not just the percentage change.
There are no extra taxes or service charges considered in this calculation.

Concept / Approach:
Revenue is equal to price multiplied by quantity. Since quantity remains constant, the revenue is directly proportional to the ticket price. The ratio 9:10 tells us that the new price is (10/9) times the old price. We first compute the original revenue using the original price and number of tickets. Then we compute the new revenue using the new price and the same number of tickets. The increase is simply the difference between these two revenue values.

Step-by-Step Solution:
Original price per ticket = Rs. 180. Number of tickets sold = 2,200. Original revenue = 180 * 2,200 = 396,000 rupees. The price ratio 9:10 means new price = (10/9) * 180. Compute new price: (10/9) * 180 = 200 rupees per ticket. New revenue = 200 * 2,200 = 440,000 rupees. Increase in revenue = 440,000 - 396,000 = 44,000 rupees.

Verification / Alternative check:
Instead of calculating both revenue values separately, we can use proportionality. Since the price changes from 9 parts to 10 parts, revenue also changes from 9 parts to 10 parts. So 1 part of revenue equals 396,000 / 9 = 44,000. The extra one part gained due to the price increase is therefore 44,000, matching our detailed calculation.

Why Other Options Are Wrong:
Option 440000 represents the new revenue itself, not the increase; the question asks for the difference between new and old revenue.
Option 39600 is much smaller than one ninth of 396,000, so it cannot represent the correct incremental part in the 9:10 ratio.
Option 396000 is exactly the original revenue, not the increase, so it does not answer the question asked.

Common Pitfalls:
Students sometimes confuse the increased revenue with the new total revenue and select 440,000 instead of the increment 44,000.
Another mistake is to apply the 9:10 ratio to the number of tickets instead of the price, which is not what the question states.
Some learners also forget that the number of tickets sold stays the same and unnecessarily alter both price and quantity.

Final Answer:
The increase in the cinema hall's total revenue is Rs. 44,000.