Two trains running in opposite directions cross a man standing on the platform…
2025
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
- A.
1 : 3
- B.
3 : 2
- C.
3 : 4
- D.
None of these
Attempted by 9 students.
Show answer & explanation
Correct answer: B
Concept: When a train crosses a stationary object such as a man, the distance it covers equals its own length, so length = speed × time taken to cross that object. When two trains moving in opposite directions cross each other completely, the time taken equals (sum of their lengths) ÷ (sum of their speeds), because their speeds add up when moving toward each other.
Let the speed of the first train be sA and the speed of the second train be sB.
Length of the first train, which crosses the man in 27 seconds: LA = 27 × sA.
Length of the second train, which crosses the man in 17 seconds: LB = 17 × sB.
When the two trains cross each other, the relative speed is sA + sB, and the time taken is 23 seconds, so (LA + LB) ÷ (sA + sB) = 23.
Substituting: (27 sA + 17 sB) ÷ (sA + sB) = 23, which gives 27 sA + 17 sB = 23 sA + 23 sB, so 4 sA = 6 sB, so sA ÷ sB = 6/4 = 3/2.
Cross-check: Taking sA = 3k and sB = 2k gives train lengths of 81k and 34k; the combined length 115k divided by the combined speed 5k gives exactly 23 seconds, confirming the ratio 3 : 2.
Result: So the ratio of their speeds is 3 : 2.