Question

A train moving at 108 km/hr crosses a platform in 30 seconds. Then it crosses a man running at 12 km/hr in the same direction in 9 seconds. What is the length of train and platform in m?

• A. \(240 \text{ } and 660 \text{}\)
• B. \(200 \text{ } and 620 \text{}\)
• C. \(220 \text{ } and 600 \text{}\)
• D. \(250 \text{ } and 640 \text{}\)

Hint:

When converting speeds for these calculations, remember to convert km/hr to m/s by multiplying by \(\frac{1000}{3600}\).

Answer 1

The Correct Option is C

Step 1: Calculate the length of the train.
The train's speed relative to the man is \( 108 - 12 = 96 \) km/hr, which is \( 96 \times \frac{1000}{3600} = 26.67 \) m/s. \[ \text{Length of train} = 26.67 \text{ m/s} \times 9 \text{ s} = 240 \text{ m} \]

Step 2: Calculate the total length covered when crossing the platform.
The train's speed in m/s is \( 108 \times \frac{1000}{3600} = 30 \) m/s. \[ \text{Total length} = 30 \text{ m/s} \times 30 \text{ s} = 900 \text{ m} \] \[ \text{Length of platform} = 900 - 240 = 660 \text{ m} \]