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:

Time taken to cross in same direction = 72 second

Time taken to cross in opposite direction = 18 second

Speed of train X = 60 km/hr = 60 $$\times$$ \frac{5}{18}$$ = 16.66 m/sec

Length of train Y = 225 m

Let the length of train X be l m and speed of train Y be x m/sec.

Total length = (225 + l) m

Relative speed when trains run opposite direction = (16.66 + x) m/sec

Length = speed $$\times time$$

225 + l = (16.66 + x) $$\times$$ 18

225 + l = 300 + 18x

l = 75 + 18x ---(1)

Relative speed when trains run opposite direction = (16.66 - x) m/sec

225 + l = (16.66 - x)  $$\times$$ 72

225 + l = 1200 - 72x

l = 975 - 72x ---(2)

By eq(1) and (2),

75 + 18x = 975 - 72x

90x = 900

x = 10 m/sec

Speed (in km/h) of Y = 10 $$\times$$ \frac{18}{5} = 36 km/hr

Put the value of x in eq(1)

l = 75 + 18 $$\times$$ 10 = 255 m