Introduction / Context:
This question tests a basic but important application of ratios to percentage or absolute changes. Instead of directly specifying a percentage increase, the problem states that the flight fare increases in the ratio 11 : 13. You need to translate this ratio information into an actual increase in rupees, given the original fare. Such questions help develop comfort with using ratios to compare old and new values.
Given Data / Assumptions:
- Original fare between two cities = Rs 12,100.
- The ratio of old fare to new fare is 11 : 13.
- The fare is increased, so the new fare is higher than the old fare.
- We want the increase in rupees, not the new fare itself.
Concept / Approach:
When old : new = 11 : 13, it means that if the old fare is treated as 11 equal parts, the new fare is 13 of the same parts. Therefore the increase corresponds to the difference between 13 parts and 11 parts, that is 2 parts. Using the actual old fare, we compute the value of one part and then calculate the increase as 2 times that part size.
Step-by-Step Solution:
1) Let the common unit part of the fare be k.
2) Old fare = 11k and new fare = 13k.
3) We are given that the old fare is Rs 12,100, so 11k = 12,100.
4) Solve for k: k = 12,100 / 11 = 1,100.
5) Increase in fare = new fare minus old fare = 13k - 11k = 2k.
6) Therefore, increase = 2 * 1,100 = Rs 2,200.
Verification / Alternative check:
We can compute the new fare explicitly as 13k = 13 * 1,100 = Rs 14,300. Then the increase is 14,300 - 12,100 = 2,200. This matches the earlier calculation using the difference in ratio parts. Both methods agree, confirming that our understanding of the ratio 11 : 13 and the resulting increase is correct.
Why Other Options Are Wrong:
Option A (Rs 14,300) is the new fare, not the increase, and therefore answers the wrong quantity. Option C (Rs 22,000) and option E (Rs 1,100) are multiples of the base unit but do not represent the difference between the old and new fares. Option D (Rs 1,430) appears to be a miscalculation, possibly confusing the 13 in the ratio with a percentage. Only Rs 2,200 correctly represents the actual increase based on the ratio 11 : 13 with an original fare of Rs 12,100.
Common Pitfalls:
A common error is to treat the ratio 11 : 13 as direct fares and forget that the original fare must correspond to the 11-part value. Another pitfall is confusing the new fare with the increase, or incorrectly assuming that an 11 : 13 ratio describes a 13 over 11 percent increase. Always distinguish carefully between the absolute amounts (old and new) and the increment between them, and use the difference between the ratio parts (13 - 11) to represent the increase proportion.
Final Answer:
The increase in the flight fare is
Rs 2,200.
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