Question

A train travelling at a speed of 72 km/h crosses another train, having double its length and travelling in the opposite direction at a speed of 54 km/h, in 12 s. It also passes a tunnel in 40 s. What is the length (in m) of the tunnel?

• A. 580
• B. 640
• C. 660
• D. 680

Hint:

In relative speed problems, add the speeds of two objects moving towards each other. Multiply by time to get the total distance covered, and subtract the lengths of the objects to find the remaining distance (like the tunnel).

Answer 1

The Correct Option is C

Let the length of the train be \( L \).
The speed of the first train is 72 km/h, or \( 72 \times \frac{5}{18} = 20 \, \text{m/s} \).
The speed of the second train is 54 km/h, or \( 54 \times \frac{5}{18} = 15 \, \text{m/s} \).
The relative speed of the two trains is \( 20 + 15 = 35 \, \text{m/s} \).
The two trains cross each other in 12 s, so the total length of the two trains is:
\[ 35 \times 12 = 420 \, \text{m} \] Since the second train has double the length of the first train, the length of the first train is \( \frac{420}{3} = 140 \, \text{m} \).
Thus, the length of the second train is \( 2 \times 140 = 280 \, \text{m} \).
Now, the total length of both trains is \( 140 + 280 = 420 \, \text{m} \). The time taken to pass the tunnel is 40 s.
So, the length of the tunnel is: \[ \text{Length of the tunnel} = \text{Speed of the first train} \times \text{Time to pass the tunnel} - \text{Length of the first train} \] \[ \text{Length of the tunnel} = 20 \times 40 - 140 = 800 - 140 = 660 \, \text{m} \] Thus, the length of the tunnel is 660 meters.