Train A travelling at 126 km/ hour speed, completely crosses Train B in 9 seconds. Train B is half the length of Train A and is travelling at a speed of 90 km/ hour in the opposite direction (towards Train A). How much will Train A take to cross a platform of length 690 metres ?

Let length of train B = $$x$$ m

=> Length of train A = $$2x$$ m

Speed of train A = 126 km/h = $$126 \times \frac{5}{18} = 35$$ m/s

Speed of train B = 90 km/h = $$90 \times \frac{5}{18} = 25$$ m/s

Since, the trains are moving in opposite direction, relative speed = 35 + 25 = 60 m/s

Time taken = 9 sec

=> $$\frac{2x + x}{60} = 9$$

=> $$3x = 9 \times 60 = 540$$

=> $$x = \frac{540}{3} = 180$$ m

Thus, length of train A = 360 m

$$\therefore$$ Time taken by train A take to cross a platform of length 690 metres

= $$\frac{360 + 690}{35} = \frac{1050}{35}$$

= $$30$$ seconds