Question

Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hr. The faster train passes the slower train in 36 sec. The length of each train is

• A. 50 m
• B. 80 m
• C. 72 m
• D. 82 m

Answer 1

The Correct Option is A

The correct option is (A): 50 m
Explanation: To find the length of each train, we can use the relative speed of the trains and the time taken to pass each other.
Convert speeds from km/h to m/s:
- Speed of the faster train: \(46 \text{ km/h} = \frac{46 \times 1000}{3600} = \frac{46000}{3600} \approx 12.78 \text{ m/s}\)
  - Speed of the slower train: \(36 \text{ km/h} = \frac{36 \times 1000}{3600} = \frac{36000}{3600} = 10 \text{ m/s}\)
Calculate the relative speed:
  Since the trains are moving in the same direction, the relative speed is the difference of their speeds:
  \[\text{Relative speed} = 12.78 \text{ m/s} - 10 \text{ m/s} = 2.78 \text{ m/s}\]
Use the time to calculate the length:
  The time taken to pass each other is 36 seconds. In this time, the faster train covers a distance equal to the combined lengths of the two trains.
  \[\text{Distance} = \text{Relative speed} \times \text{Time} = 2.78 \text{ m/s} \times 36 \text{ s} = 100.08 \text{ m}\]
Since the distance covered is equal to the length of both trains:
  \[2L = 100.08 \implies L = \frac{100.08}{2} = 50.04 \text{ m}\]
Therefore, the length of each train is approximately 50 m.