Introduction / Context:
This is a straightforward ratio-based fare increase question. Instead of specifying a percentage, the problem tells you that the bus fare increases in the ratio 1 : 2. With the original fare known, you must determine how much the fare has increased in rupee terms. Such problems reinforce the interpretation of ratios as comparisons between old and new values.
Given Data / Assumptions:
- Old fare between two cities = Rs 175.
- Ratio of old fare to new fare = 1 : 2.
- The fare is increased, so the new fare is higher than the old fare.
- We need the increase in rupees, not simply the new fare.
Concept / Approach:
If old : new = 1 : 2, it means that the new fare is twice the old fare. The increase in fare is the difference between the new and old values. Therefore, after computing the new fare from the ratio, we subtract the old fare to find the increase. This is a direct application of interpreting ratios as multiplicative comparisons.
Step-by-Step Solution:
1) Let the common unit part of the fare be k.
2) Old fare = 1k and new fare = 2k.
3) Given that old fare = Rs 175, so 1k = 175, hence k = 175.
4) New fare = 2k = 2 * 175 = Rs 350.
5) Increase in fare = new fare - old fare = 350 - 175.
6) Therefore, increase in fare = Rs 175.
Verification / Alternative check:
We can interpret the ratio 1 : 2 as indicating the new fare is 100 percent more than the old fare. Since 100 percent of 175 is again 175, the increase should be Rs 175. Adding this to the original fare 175 gives 350, which matches our earlier calculation of the new fare. Both the ratio interpretation and the direct multiplication agree on the same increase value.
Why Other Options Are Wrong:
Option A (Rs 350) is the new fare itself, not the increase. Option B (Rs 70) would correspond to an increase of only 40 percent, which does not match the ratio 1 : 2. Option C (Rs 140) is also inconsistent, as that would give a new fare of 315, not in the ratio 1 : 2 with 175. Option E (Rs 90) is a random value that does not support the given ratio. Only Rs 175 correctly represents the increase implied by the ratio 1 : 2 applied to an original fare of 175.
Common Pitfalls:
One common error is confusing the ratio 1 : 2 with a 2 percent or small percentage increase, or misinterpreting the ratio as 1 part extra instead of the entire new value being 2 parts. Learners may also forget to subtract the old fare to find the increase and instead report the new fare directly. Always separate the steps of finding the new value from finding the increase or decrease, and interpret ratios clearly.
Final Answer:
The increase in bus fare is
Rs 175.
Discussion & Comments