Two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 33 seconds. The ratio of their speeds is:

Question: Two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 33 seconds. The ratio of their speeds is:

Solution:
Let,
The speed of the 1st train be x m/sec
The speed of the 2nd train be y m/sec

∴ Length of the 1st train = 37x metres
∴ Length of the 2nd train = 27y metres

ATQ,
(37x + 27y)/(x + y) = 33 [ time = distance/speed]
⇒ 37x + 27y = 33x + 33y
⇒ 37x - 33x = 33y - 27y
⇒ 4x = 6y
⇒ 2x = 3y
⇒ x/y = 3/2
∴ x : y = 3 : 2