Fare ratio vs passenger ratio with total collection: The 1st-class to 2nd-class train fare ratio between two stations is 3 : 1. The number of passengers in 1st : 2nd class is 1 : 50. If ₹ 2650 was collected in total on a day, find the amount collected from 2nd-class passengers.

Introduction / Context: Revenue equals fare * number of passengers. With two classes, express each revenue using the given ratios, sum to the total, and solve for the fare unit. Then compute the second-class revenue directly from its share.

Given Data / Assumptions:

• Fare ratio (1st : 2nd) = 3 : 1 ⇒ fares = 3k and k.
• Passenger ratio (1st : 2nd) = 1 : 50.
• Total collection = ₹ 2650.

Concept / Approach: Revenue_1st = 3k * 1 = 3k; Revenue_2nd = k * 50 = 50k. Total = 3k + 50k = 53k. Solve for k and then find the second-class revenue 50k.

Step-by-Step Solution:

Verification / Alternative check: First-class collection = 3k = 150; 150 + 2500 = 2650, matching the total.

Why Other Options Are Wrong: ₹ 2800, ₹ 3000, ₹ 3500, ₹ 2000 are not equal to 50/53 of the total and fail the ratio constraints.

Common Pitfalls: Multiplying the fare and passenger ratios together incorrectly; remember revenue is the product for each class, then sum.

Final Answer: ₹ 2500