A train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of Y are, respectively:

255 and 36

Let length of train X = a meter & speed of train Y = S km/h

According to question ,

\(\frac{225 + a }{60 - S}\) = 72   ----(1)

in 2nd case ,

\(\frac{225 + a }{60 + S}\) = 18   ----(2)

Multiply equation 2 by 4

\(\frac{4(225 + a) }{60 + S}\) = 72   ----(3)

By observing equation 1 and 3

\(\frac{225 + a }{60 - S}\) = \(\frac{4(225 + a) }{60 + S}\)

4(60-S) = (60+S)

240 - 4S = 60 + S

180 = 5S

S = 36

So , Speed of train Y = 36 km/h

Length of train ,

\(\frac{(225 + a) }{60 - 36}\)= 72

225 + a = 72 × 24 km/h

225 + a = 72 × 24 ×\(\frac{(5) }{18}\)

a = 480 - 225

a = 255 m

So , length of train X = 225 m