Explanation given by my Mathematics teacher:
Let the speed be x metres/second & let the length of the train be y metres.
(A) Train crossed signal post in 18seconds, which gives the 1st equation, 18x=y
(B) Train crossed 750m long platform in 48 seconds.
For...
more... crossing platform, we have to take into account not only length of the platform but also add the length of the train. As you know, entering platform means the engine entered and leaving platform means the guard coach left it. So this give us the 2nd equation, 48x = y+750
Solving these two equations, 2nd equation minus 1st gives 30x = 750
Therefore Speed of train, x = 750/30 = 25metres/second or 90kmph
Length of train, y = 18x = 18*25 = 450metres.
Thank you all for giving this opportunity to entertain you with a maths puzzle 35 years later.