The bus fare between two cities is increased in the ratio 17 : 20. If the original bus fare is Rs. 425, what is the increase in the fare in rupees?

Introduction / Context:
This is another example of a ratio based price change question, here applied to bus fare. The problem checks understanding of how to compute a new value when an old value is scaled according to a ratio and how to find the absolute difference between the new and old values, which represents the increase in fare.

Given Data / Assumptions:

• Original bus fare between the two cities is Rs. 425.• The fare is increased in the ratio 17 : 20.• This means the old fare corresponds to 17 parts and the new fare corresponds to 20 parts.• We are required to find the increase in fare, not the final fare.

Concept / Approach:
If a quantity changes from a ratio of a to b, the new value is (b / a) times the old value. Here, the ratio 17 : 20 indicates that the bus fare has been multiplied by 20 / 17. Once we compute the new fare as original fare multiplied by 20 / 17, the increase is obtained by subtracting the original fare from this new value. This approach directly uses the definition of ratios to avoid confusion with percentage calculations.

Step-by-Step Solution:
Step 1: Let the old fare correspond to 17 parts and the new fare correspond to 20 parts.Step 2: The scaling factor for the new fare is therefore 20 / 17.Step 3: Original fare is Rs. 425.Step 4: New fare = 425 * 20 / 17.Step 5: First compute 425 / 17. Since 17 * 25 = 425, 425 / 17 = 25.Step 6: Multiply this by 20 to get the new fare: 25 * 20 = 500.Step 7: Increase in fare = new fare − old fare = 500 − 425 = Rs. 75.

Verification / Alternative check:
We can verify by checking whether old and new fares are in the ratio 17 : 20. Divide both fares by 25. Old fare 425 / 25 = 17 and new fare 500 / 25 = 20. So the ratio is 17 : 20, which matches the given condition. This confirms that the new fare is Rs. 500 and therefore the increase of Rs. 75 is correct.

Why Other Options Are Wrong:
• Rs. 100: This would make the new fare 525, and 425 : 525 when simplified does not yield 17 : 20.• Rs. 200: This would make the new fare 625, giving a ratio inconsistent with 17 : 20.• Rs. 500: This would imply the old fare was zero, which is impossible in this context.

Common Pitfalls:
Some students mistakenly think the ratio 17 : 20 refers to a 3 part increase and directly compute an increase as 3 * 25 = 75 without justifying the part value, or they confuse ratio with percent. Others might try to compute the percentage increase from 17 to 20 and then apply that percentage incorrectly. Errors can also occur if they miscalculate 425 / 17 or forget that the question asks for the increase, not the final fare. Keeping the focus on the multiplicative factor 20 / 17 and carefully subtracting the original value helps avoid mistakes.

Final Answer:
The increase in bus fare is Rs. 75.