The flight fare between two cities is increased in the ratio 9 : 11. If the original one way air fare was Rs. 18,000, what is the increase in the fare in rupees?

Introduction / Context:
This question is about ratio and proportion applied to a real life situation involving an increase in flight fare. The idea is to understand how a price changes when it is scaled by a given ratio and then compute the absolute increase in rupee terms, which is a very common type of aptitude test question.

Given Data / Assumptions:

• Original flight fare between the two cities is Rs. 18,000.• The fare is increased in the ratio 9 : 11.• The ratio 9 : 11 means the new fare corresponds to 11 parts while the old fare corresponds to 9 parts.• We are required to find the increase in fare, that is, new fare minus old fare.

Concept / Approach:
If a quantity changes from a ratio of a to b, it means the new value is (b / a) times the old value. Here, the fare changes from 9 parts to 11 parts. So, new fare = old fare * (11 / 9). Once we find the new fare using this scaling factor, the increase is simply new fare minus old fare. This method avoids any confusion between percentage increase and ratio increase by directly using the proportional relation.

Step-by-Step Solution:
Step 1: Let the old fare correspond to 9 parts, so new fare corresponds to 11 parts.Step 2: The scaling factor for the new fare is 11 / 9.Step 3: Compute the new fare using the old fare of Rs. 18,000.Step 4: New fare = 18,000 * 11 / 9.Step 5: First divide 18,000 by 9 to simplify: 18,000 / 9 = 2,000.Step 6: Now multiply 2,000 by 11: 2,000 * 11 = 22,000.Step 7: Therefore, the new fare is Rs. 22,000.Step 8: The increase in fare = new fare − old fare = 22,000 − 18,000 = Rs. 4,000.

Verification / Alternative check:
We can check whether the new fare and old fare are indeed in the ratio 9 : 11. Divide both fares by 2,000. Old fare 18,000 / 2,000 = 9 and new fare 22,000 / 2,000 = 11. So the ratio is 9 : 11 as required. This confirms that the calculation is correct and the increase of Rs. 4,000 is consistent with the described change in ratio.

Why Other Options Are Wrong:
• Rs. 3,600: This value might be obtained if someone incorrectly applies a percentage calculation instead of the exact ratio scaling.• Rs. 2,000: This would correspond to a smaller increase and does not satisfy the required 9 : 11 ratio for old and new fares.• Rs. 2,200: This is also not consistent with the proportional relation between 18,000 and 22,000 implied by 9 : 11.

Common Pitfalls:
Many learners confuse ratio increase with a simple percentage increase and may try to compute the percentage change directly from 9 to 11 as if it were a percentage. Another common mistake is to add or subtract numbers from the ratio instead of using them as multiplicative factors. Some candidates also forget to compute the difference between new and old fare and instead mark the new fare itself as the answer. Being clear about whether the question asks for the new value or just the increase is very important.

Final Answer:
The increase in flight fare is Rs. 4,000.