A train X travelling at 72 km/h crosses another train Y travelling at 63 km/h (in opposite direction) in 18 seconds. If the length of train Y is two-third the length of X, then the length of train X is:

If the length of train Y is two-third the length of X.

Let's assume the length of train X is 3a.

length of train Y = $$\frac{2}{3}\times\ 3a$$ = 2a

A train X travelling at 72 km/h crosses another train Y travelling at 63 km/h (in opposite direction) in 18 seconds.

$$\frac{3a+2a}{18}\ =\ \frac{(72+63)\times1000}{3600}$$

$$\frac{5a}{18}\ =\ \frac{135\times10}{36}$$

$$a\ =\ \frac{27\times10}{2}$$

$$a\ =\ 27\times5$$

a = 135

Length of train X = 3a

= $$3\times135$$

= 405 m