The bus fare between two cities is increased in the ratio 11 : 18. What will be the increase in the fare if the original fare was Rs. 550?

Introduction / Context:
This is a simple ratio-based price increase problem. We are told that the fare between two cities increases such that the ratio of the old fare to the new fare is 11 : 18. Given the original fare, we must compute the new fare and then the absolute increase. This tests the ability to interpret fare changes expressed in ratio form instead of a direct percentage.

Given Data / Assumptions:

• Original fare : New fare = 11 : 18.
• Original fare = Rs. 550.
• We must find the increase in fare in rupees.

Concept / Approach:
Since original fare corresponds to the ratio part 11 and new fare corresponds to ratio part 18, we first determine what one ratio unit corresponds to in rupees. That is done by dividing the original fare by 11. Then we multiply this unit by 18 to get the new fare. The increase is new fare minus original fare. This is a standard way of using ratios to scale from one value to another.

Step-by-Step Solution:

Verification / Alternative check:
Check that the ratio of old to new fare matches the given ratio. Old : New = 550 : 900. Divide by 50 to simplify: 11 : 18, which is exactly the ratio specified in the question. Therefore, our value for the new fare and the increase is consistent.

Why Other Options Are Wrong:

• Rs. 900 is the new fare itself, not the increase.
• Rs. 180 and Rs. 360 do not correspond to the difference between 550 and any new fare that is in the ratio 11 : 18 with 550.

Common Pitfalls:
Some students mistakenly treat 11 : 18 as a percentage and try to compute a percentage increase directly, which leads to incorrect values. Another error is to incorrectly scale the fare by 18/11 but then forget to subtract the original fare to find the increase. Always separate the steps: compute the new fare from the ratio, then subtract to get the increase.

Final Answer:
The increase in fare is Rs. 350.