Train Station Puzzle

Two Village Puzzles

The Train Station Puzzle on this page has a scenario where a man had two houses, one in village A and another in village B. He worked at a factory, in a city, which is located somewhere between the two villages. There was a train station near his factory and he would take a train back home every night to either village A or village B, depending on which one he got first. There were plenty of trains scheduled for both the villages, however, the man realized that most of the time he would end up on the train to village B, and hardly he got on a train to village A.

The man does not have a fixed schedule and he arrives at the train station at random times, so why do you think he gets the train to village B more than A?

train station puzzle

Solution of Train Station Puzzle

According to the puzzle, there are ample trains destined for both stations, however, he got a train to village B more than a train to village A. The man has no fixed schedule, therefore we can say that no matter when he came to the station, the train to village B was available more frequently than that to village A.
From the above, let us assume a train schedule, as given below:-

Train to village B:- arrives at 12:50pm

Train to village A:- arrives at 12:52 pm

Train to village B:- arrives at 1:00 pm

Train to village A:- arrives at 1:02 pm

Train to village B:- arrives at 1:10pm

Train to village A:- arrives at 1:12 pm

Train to village B:- arrives at 1:20 pm

Train to village A:- arrives at 1:22 pm

Train to village B:- arrives at 1:30pm

Train to village A:- arrives at 1:32 pm

Train to village B:- arrives at 1:40 pm

Train to village A:- arrives at 1:42 pm

Now let us assume that the man reaches the station anytime between 1:13 pm- 1:20 pm he will get the train to village B, while if he arrives between 1:10 pm-1:12 pm he will get the train to village A. It shows that there is a window of 7 minutes for him to board the train to village B while only a window of 2 minutes to get to village A.

Similarly, throughout the day, the window for getting the train to village B is higher than that of getting a train to village A, and therefore the man frequents village B more than A.

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