Understanding the Problem: Train Crossing a Platform

This question asks us to find the speed of a train in kilometers per hour (kmph). We are given the length of the train, the length of the platform it crosses, and the time taken to cross it.

When a train crosses a platform, the total distance covered by the train is equal to the sum of its own length and the length of the platform.

Calculating the Total Distance Covered

The length of the train is given as 275 metres.

The length of the platform is equal to the length of the train, so it is also 275 metres.

Total distance covered by the train while crossing the platform = Length of train + Length of platform

Total distance = $\text{275 metres} + \text{275 metres} = \text{550 metres}$

Calculating the Speed in Metres per Second (m/s)

The time taken to cross the platform is 33 seconds.

We can calculate the speed using the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Speed = $\frac{\text{550 metres}}{\text{33 seconds}}$

Speed = $\frac{550}{33} \text{ m/s}$

Converting Speed from m/s to kmph

The question requires the speed in kilometers per hour (kmph).

To convert speed from metres per second (m/s) to kilometers per hour (kmph), we multiply the speed in m/s by the conversion factor $\frac{18}{5}$.

Conversion factor: $\text{1 m/s} = \frac{18}{5} \text{ kmph}$

Speed in kmph = Speed in m/s $\times \frac{18}{5}$

Speed in kmph = $\frac{550}{33} \times \frac{18}{5}$

Simplifying the Calculation

We can simplify the expression:

• Divide 550 by 5: $\frac{550}{5} = 110$
• Divide 18 by 33 (by dividing both by 3): $\frac{18}{33} = \frac{6}{11}$

So, the expression becomes:

Speed in kmph = $110 \times \frac{6}{11}$

Now, divide 110 by 11:

$\frac{110}{11} = 10$

Speed in kmph = $10 \times 6 = 60$ kmph

Final Answer

The speed of the train is 60 kmph.