Math Puzzle: Maximum Stations for 50 Metro Passengers
A Dhaka Metro Rail carriage has 50 passengers who boarded from various stations. The question asks for the maximum number of stations from which these passengers could have boarded, given that at least 3 passengers boarded from each station. To maximize the number of stations, we assume the minimum number of passengers boarded from each station, which is 3. Therefore, we divide the total number of passengers (50) by the minimum number of passengers per station (3). 50 divided by 3 equals 16 with a remainder of 2. This means that 16 stations could have contributed 3 passengers each, accounting for 16 * 3 = 48 passengers. The remaining 2 passengers must have boarded from an additional station. Thus, the maximum number of stations from which the 50 passengers could have boarded is 16 + 1 = 17 stations.
This problem presents a simple division scenario disguised as a real-world scenario. It highlights how mathematical constraints can be applied to logistical situations. The core principle is to determine the maximum number of contributing sources (stations) given a fixed total (passengers) and a minimum contribution per source. The solution demonstrates that by minimizing individual contributions, the number of sources can be maximized, a concept applicable in resource allocation and network analysis. Understanding these basic mathematical relationships is crucial for efficient planning in transportation and other systems.
AI-generated to prompt reflection — not editorial opinion, not advice, not a statement of fact. How this works.