At 60% of its usual speed, a train of length L metres crosses a platform 240 metre long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in metre)?

Let speed of the train = $$10x$$ m/s

Length of train = $$l$$ m

Time taken to cross the pole = 6 sec

Using, $$speed = \frac{distance}{time}$$

=> $$10x = \frac{l}{6}$$

=> $$x = \frac{l}{60}$$

Now, 60% of the speed = $$\frac{60}{100} \times 10x = 6x$$ m/s

Length of platform = 240 m

Acc. to ques, => $$6x = \frac{240 + l}{15}$$

=> $$6 \times \frac{l}{60} = \frac{240 + l}{15}$$

=> $$\frac{l}{10} = \frac{240 + l}{15}$$

=> $$15l = 2400 + 10l$$

=> $$15l - 10l = 5l = 2400$$

=> $$l = \frac{2400}{5} = 480$$ m