Two trains running in opposite directions cross a man standing on the platform…
2024
Two trains running in opposite directions cross a man standing on the platform in 32 seconds and 25 seconds respectively and they cross each other in 28 seconds. The ratio of their speeds is:
- A.
2:3
- B.
1:4
- C.
3:2
- D.
3:4
Attempted by 10 students.
Show answer & explanation
Correct answer: D
Final ratio: 3:4
Let v1 and v2 be the speeds of the two trains, and L1 and L2 their lengths.
From the times to pass a man: L1 = 32·v1 and L2 = 25·v2.
When the trains cross each other (opposite directions): (L1 + L2) / (v1 + v2) = 28.
Substitute L1 and L2: (32·v1 + 25·v2) / (v1 + v2) = 28 ⇒ 32v1 + 25v2 = 28v1 + 28v2.
Rearrange: 32v1 − 28v1 = 28v2 − 25v2 ⇒ 4v1 = 3v2, so v1/v2 = 3/4.
Therefore the ratio of their speeds is 3:4.