Between two stations, first-class and second-class fares are in the ratio 4 : 1, while the number of first-class to second-class passengers is 1 : 40. If the total fare collected is Rs. 1100, how much is collected from first-class passengers?

Introduction / Context:
Total fare depends on both the fare per passenger and the number of passengers. Multiply the fare ratio by the passenger ratio to get revenue “parts” from each class, then proportion the actual total accordingly.

Given Data / Assumptions:

• Fare ratio (first : second) = 4 : 1
• Passenger ratio (first : second) = 1 : 40
• Total revenue = Rs. 1100

Concept / Approach:
Revenue parts: First-class contributes 4 * 1 = 4 parts; second-class contributes 1 * 40 = 40 parts. Total revenue parts = 44. The first-class share is 4/44 of the total.

Step-by-Step Solution:
Revenue parts: First = 4*1 = 4; Second = 1*40 = 40Total parts = 4 + 40 = 44First-class revenue = (4/44) * 1100 = Rs. 100

Verification / Alternative check:
Second-class revenue = (40/44)*1100 = Rs. 1000; adding to 100 gives Rs. 1100, matching the total.

Why Other Options Are Wrong:
Other amounts do not equal 4/44 of 1100; they would misallocate the proportional shares.

Common Pitfalls:
Adding ratios or averaging instead of multiplying fare and passenger ratios; forgetting that revenue is fare × count.

Final Answer:
Rs. 100