Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Step 1: Understand the given data

• Length of each train = 120 meters
• Time taken by first train to cross a pole = 10 seconds
• Time taken by second train to cross a pole = 15 seconds

Step 2: Calculate the speed of each train

Speed = Distance / Time

Speed of Train A = 120 / 10 = 12 m/s
Speed of Train B = 120 / 15 = 8 m/s

Step 3: Find the relative speed

Since the trains are moving in opposite directions, their relative speeds will be added:

Relative speed = 12 + 8 = 20 m/s

Step 4: Total distance to be covered when trains cross each other

Each train is 120 m long, so total distance = 120 + 120 = 240 meters

Step 5: Calculate the time to cross each other

Time = Total Distance / Relative Speed = 240 / 20 = 12 seconds

Answer: 12 seconds

The two trains will cross each other in 12 seconds when moving in opposite directions.

This question demonstrates how the concept of relative speed applies when two moving bodies travel toward each other. It’s a commonly tested topic in time-speed-distance problems found in competitive exams.