Two trains running in opposite directions cross a man standing on the platform 54s and 34s respectively and they cross each other in 46 s . Find the ratio of their speeds.?

Let the speeds of two trains be x and y, respectively .
∴ Length of 1st train = 54x
Length of the 2nd train = 34y
According to the question.
(54x + 34y) / (x + y) = 46
⇒ 54x + 34y = 46x + 46y
⇒ 27x + 17y = 23x + 23y
⇒ 4x = 6y
⇒ x/y = 3/2
∴ x : y = 3 : 2