When the taxi is just about to leave there will be taxis coming from the opposite side;Our taxi will surely meet those taxis. So, no. of taxis which will be in the path are:[(total time each taxi takes to reach destination)/(total time after which each taxi leaves the station)] + 1In this case it is:120/10 + 1= 12+1=13(+1 as we need to take both the last and the first taxi).So, we have total of 13 taxis on the path out of which we will subtract 1 as we are not considering the taxi meeting station Y.Now, we need to calculate the no. of taxis which leave after our taxi leaves;Those will be again:[(total time each taxi takes to reach destination)/(total time after which each taxi leaves the station)] +1in our case it is120/10 + 1= 12+1=13(+1 as we need to take both the last and the first taxi).Now, we will subtract 2 as we have counted the taxi which will leave station X when our taxi leaves station Y twice and also as we are not considering the taxi meeting station X.So, now we have a total of 12+11=23 taxis coming from other side which each taxi will meet enroute from Y to X.

2hr=120min.within this time both taxi will leave the station for 12 times nd come back for 11 times.as both taxis are moving simultaneously they will cross each other for 23 times.

Introduction:

In this scenario, we have two taxis traveling between two stations, X and Y. They leave their respective stations every 10 minutes and travel at the same constant speed. The distance between the two stations is covered by each taxi in 2 hours. We need to determine how many taxis coming from the other side each taxi will meet en route from Y to X.

Analysis:

To solve this problem, let's consider the time it takes for a taxi to travel between the two stations. Each taxi takes 2 hours to complete the journey, which is equivalent to 120 minutes.

Calculating the number of taxis:

1. First, we need to find the number of taxis that leave each station in 120 minutes. Since a taxi leaves every 10 minutes, we can divide the total time (120 minutes) by the time interval between each taxi departure (10 minutes).

Number of taxis leaving from station X = 120 minutes / 10 minutes = 12 taxis
Number of taxis leaving from station Y = 120 minutes / 10 minutes = 12 taxis

Therefore, there are 12 taxis leaving from each station in a span of 120 minutes.

2. Now, let's consider the scenario where a taxi leaves from station X. For this taxi to meet a taxi coming from the other side (station Y) while traveling from Y to X, it needs to encounter the taxis that left from station Y during the 120-minute journey.

a. The first taxi leaving from station Y will take 10 minutes to reach the halfway point between the two stations. At this point, the taxi from station X will have traveled for 10 minutes.
b. The second taxi leaving from station Y will take 20 minutes to reach the halfway point, and the taxi from station X will have traveled for 20 minutes.
c. This pattern continues, and for each taxi leaving from station Y, the taxi from station X will have traveled an additional 10 minutes.

Therefore, the number of taxis coming from the other side (station Y) that each taxi from station X will meet en route from Y to X is equal to the number of taxis leaving from station Y in a span of 120 minutes, which is 12 taxis.

Conclusion:

Each taxi leaving from station X will meet 12 taxis coming from the other side (station Y) while traveling from Y to X. This is because the taxis leave at the same constant speed and every 10 minutes, and the total journey time is 2 hours.