A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Let the length of the train be x metres and its speed be y m/sec.

Then, $$\frac{x}{y} = 15$$ ⇒ $$y = \frac{x}{15}$$

∴ $$\frac{x + 100}{25} = \frac{x}{15}$$

⇒ 15(x + 100) = 25x

⇒ 15x + 1500 = 25x

⇒ 1500 = 10x

⇒ x = 150 m.