Question

A train travelling at 48 km/h completely crosses another train having half the length of first train and travelling in opposite direction at 42 km/h in 12 seconds. The train having speed 48 km/h also passes a railway platform in 45 seconds. What is the length of the platform?

• A. 600m
• B. 300m
• C. 400m
• D. 200m

Answer 1

The Correct Option is C

To solve this problem, we need to find the length of the platform. Let's start by determining the length of the train traveling at 48 km/h and then use it to calculate the platform length.

First, convert the speeds from km/h to m/s: 

• Speed of first train (Train A) = 48 km/h = \(\frac{48 \times 1000}{3600} = 13.33\) m/s
• Speed of second train (Train B) = 42 km/h = \(\frac{42 \times 1000}{3600} = 11.67\) m/s

Since the trains are moving in opposite directions, their relative speed is the sum of their speeds:

\(13.33 + 11.67 = 25\) m/s

Let the length of Train A be \(L\). The length of Train B is half of Train A, so it is \(\frac{L}{2}\).

The time taken to cross each other is 12 seconds. Using the relative speed and the total length covered (sum of lengths of both trains), we can write:

\(L + \frac{L}{2} = 25 \times 12\)

Simplifying the equation:

\(\frac{3L}{2} = 300\)

Solving for \(L\):

\(3L = 600\)
\(L = 200\) meters

The length of Train A is 200 meters.

Now, calculate the length of the platform. Train A crosses a platform in 45 seconds. The speed of Train A is 13.33 m/s, so the total distance covered when crossing the platform is:

\(200 + \text{Length of platform} = 13.33 \times 45\)

Simplifying:

\(200 + \text{Length of platform} = 600\)

Therefore, the length of the platform is:

\(600 - 200 = 400\) meters

Hence, the correct answer is 400 meters.