A student is standing on a railway station. A train is coming towards him. The first two carriages is passed her in 2seconds and next two is passed in 2.4 seconds. The train is uniformly decelerating. When the train stops the student is standing in front of the last carriage. How many carriages are there in the train?

To find the number of carriages in the train, we need to analyze the given information. Let's break down the problem step by step:

1. First two carriages passed the student in 2 seconds.
2. Next two carriages passed the student in 2.4 seconds.
3. The train is uniformly decelerating.

Assuming that the time gap between each set of two carriages is constant, we can calculate the difference in time between the first and second sets:

Time for the first set of two carriages = 2 seconds
Time for the second set of two carriages = 2.4 seconds

Difference in time = (Time for the second set) - (Time for the first set)
Difference in time = 2.4 seconds - 2 seconds
Difference in time = 0.4 seconds

Since the train is decelerating uniformly, each set of two carriages is taking longer to pass the student. The difference in time between each set would be constant.

Now, let's assume that X is the time taken by the third set of two carriages to pass the student.

According to the given information, the difference in time is 0.4 seconds. So, X = 2.4 seconds + 0.4 seconds = 2.8 seconds.

Now we have the time taken for the third set of two carriages to pass the student, which is 2.8 seconds.

To find the total number of carriages, we can set up a proportion:

(2 carriages) / (2 seconds) = (2 carriages) / (2.8 seconds)

Cross-multiplying:

(2 carriages) * (2.8 seconds) = (2 seconds) * (2 carriages)
5.6 carriages = 4 carriages

Now, we can solve for the total number of carriages:

Let 'N' represent the total number of carriages.

(2 carriages) / (2 seconds) = (N carriages) / (2.8 seconds)

Cross-multiplying:

(2 carriages) * (2.8 seconds) = (2 seconds) * (N carriages)
5.6 carriages = 2N carriages

Dividing both sides by 2:

2.8 = N

Hence, there are approximately 2.8 carriages in the train. Since the number of carriages must be a whole number, we can conclude that there are approximately 3 carriages in the train.