The flight fare between two cities is increased in the ratio 9 : 11. If the original one-way fare was Rs 18,000, what is the increase in the ticket price (in Rs)?

Introduction / Context:
This question is a classic application of ratios and percentage increase in the context of travel fares. The fare between two cities has been increased in a specific ratio, and we are given the original ticket price. Our goal is to translate the ratio information into actual rupee values and then compute how much extra a passenger now pays after the hike. This type of question tests understanding of ratios, proportional thinking, and simple arithmetic rather than complicated algebra.

Given Data / Assumptions:
• Original flight fare between the two cities = Rs 18,000. • Ratio of old fare to new fare = 9 : 11. • We assume the ratio 9 : 11 directly compares old fare : new fare. • We need to find the increase in fare in rupees, that is, new fare minus old fare.

Concept / Approach:
The key idea is that if the old and new fares are in the ratio 9 : 11, then the new fare can be expressed as (11/9) times the old fare. Once the new fare is found, the increase is simply the difference between the new fare and the original fare. This is a direct use of the concept of proportionality based on ratios. No percentage calculation is strictly required, although we could also interpret the change as a percentage increase if desired.

Step-by-Step Solution:
Step 1: Let the old fare be represented by the ratio value 9 parts and the new fare by 11 parts. Step 2: We know the actual old fare is Rs 18,000. So 9 parts correspond to Rs 18,000. Step 3: Value of 1 part = 18,000 / 9 = Rs 2,000. Step 4: New fare corresponds to 11 parts = 11 * 2,000 = Rs 22,000. Step 5: Increase in fare = New fare − Old fare = 22,000 − 18,000 = Rs 4,000.

Verification / Alternative Check:
We can verify by checking the ratio directly. Old fare : New fare = 18,000 : 22,000. Divide both terms by 2,000 to simplify. We get 9 : 11, which matches the given ratio. This confirms that the interpretation and calculations are consistent. Therefore, the increase in fare as Rs 4,000 is correct.

Why Other Options Are Wrong:
• Rs 22,000: This is the new total fare, not the increase. It confuses the final amount with the increment. • Rs 3,600: This value might arise from a mistaken percentage calculation or incorrect ratio scaling. • Rs 20,000: This looks like another possible total fare guess, but it does not satisfy the 9 : 11 ratio with 18,000.

Common Pitfalls:
Students often misread the ratio 9 : 11 as meaning an 11 percent increase or directly subtract 9 from 11 and relate this difference incorrectly to the original amount. Another mistake is to compute the new fare correctly but forget that the question asks specifically for the increase, not the final fare. Careful reading of what is being asked is as important as the numerical work.

Final Answer:
The new fare is Rs 22,000 and the increase over the original fare of Rs 18,000 is Rs 4,000.