Time is taken by two trains running in opposite directions to cross a man…
2025
Time is taken by two trains running in opposite directions to cross a man standing on the platform in 28 seconds and 18 seconds respectively. It took 26 seconds for the trains to cross each other. What is the ratio of their speeds?
- A.
4:1
- B.
1:4
- C.
2:3
- D.
3:1
Attempted by 15 students.
Show answer & explanation
Correct answer: A
Concept: When a train crosses a stationary man (a point object), the distance it covers equals its own length. So, length of a train = its speed × the time it takes to cross the man. When two trains cross each other while moving in opposite directions, the time taken equals the sum of their lengths divided by the sum of their speeds (relative speed).
Application: Setting up the two train lengths and the relative-speed equation for opposite-direction crossing:
Let the speed of the first train (28 seconds to cross the man) be x, so its length = 28x.
Let the speed of the second train (18 seconds to cross the man) be y, so its length = 18y.
Since they cross each other in 26 seconds while moving in opposite directions: (28x + 18y) / (x + y) = 26
Simplifying: 28x + 18y = 26x + 26y
So: 2x = 8y, which gives x : y = 4 : 1
Cross-check: Taking x = 4k and y = k, the lengths are 112k and 18k, so the combined length is 130k and the relative speed is 5k. Time to cross each other = 130k / 5k = 26 seconds, matching the given data — confirming the ratio 4:1.