The bus fare between two cities is increased in the ratio 5 : 11. If the original fare was Rs. 275, what is the increase in the fare in rupees?

Introduction / Context:
This is a simple ratio application question involving an increase in bus fare. The phrase “increased in the ratio 5 : 11” means that the ratio of the old fare to the new fare is 5 : 11. Given the original fare, we need to find the absolute increase. Such questions test whether the student correctly interprets how ratios describe change in prices or fares.

Given Data / Assumptions:

• Old bus fare (original fare) = Rs. 275.
• Old fare : new fare = 5 : 11.
• We need to find the increase = new fare - old fare.

Concept / Approach:
If the ratio of old fare to new fare is 5 : 11, we can let the old fare be 5k and the new fare be 11k for some positive constant k. Since we know the actual old fare (Rs. 275), we can solve for k and then compute the new fare as 11k. The required increase is the difference between new fare and old fare. This is a direct and standard way of using ratios to move from relative values to absolute values.

Step-by-Step Solution:
Let the old fare be 5k and the new fare be 11k.Given that the old fare is Rs. 275, so 5k = 275.Solve for k: k = 275 / 5 = 55.New fare = 11k = 11 * 55 = Rs. 605.Increase in fare = new fare - old fare = 605 - 275 = Rs. 330.

Verification / Alternative check:
Check the ratio of old to new: 275 : 605.Divide both numbers by 55: (275 / 55) : (605 / 55) = 5 : 11.This confirms that the new fare is correctly related to the old fare in the ratio 5 : 11.

Why Other Options Are Wrong:
An increase of Rs. 121 or Rs. 242 would correspond to new fares of Rs. 396 or Rs. 517 respectively. The ratios 275 : 396 or 275 : 517 do not simplify to 5 : 11. Rs. 605 is the new fare, not the increase. Therefore the only correct increase that matches the given ratio and original fare is Rs. 330.

Common Pitfalls:
Some students misinterpret 5 : 11 as meaning the fare becomes 5 / 11 of the original or perhaps increases by (11 - 5) parts only. Others subtract 5 from 11 and treat 6 parts as the increase without linking back to the original 5 parts. The correct approach is to treat both old and new fares as proportional to a common factor k and then use the known old fare to determine k.

Final Answer:
The increase in bus fare is Rs. 330.