Raj likes to cross the moving train before it reaches a station 4 km away from where he is now. He starts from the end of the train and crosses it at a point 2.4 km away from the station. If he moves faster by 18 km/hr, he would cross the train at a point 3 km away from the station. If the train is moving with a speed of 54 km/hr, then what is the length of the train (in m)?

Option 4 : 400

Let their speed of the man be ‘x’ and the length of the train be ‘L’

⇒ Relative speed = x – 54

⇒ Time taken to cross = Length of train / Relative speed = L / (x – 54)

⇒ Distance travelled by the man in the same time = Speed × time

⇒ 4 – 2.4 = x × L/ (x – 54)

⇒ (1.6x – 86.4) /x = L    → 1

In second case,

⇒ Relative speed = x + 18 – 54 = x – 36

⇒ Time taken to cross = Length of train / Relative speed = L / (x – 36)

⇒ Distance travelled by the man in the same time = Speed × time

⇒ 4 – 3 = (x + 18) × L/ (x – 36)

⇒ (x – 36) / (x + 18) = L    → 2

Equating 1 and 2

⇒ (1.6x – 86.4) /x = (x – 36) / (x + 18)

⇒ 1.6x² – 57.6x – 1555.2 = x² – 36x

⇒ (0.6x² – 21.6x – 1555.2) ÷ 0.6

⇒ x² – 36x - 2592 = 0

Solving x = 72 or x = -36

Speed cannot be negative,

⇒ x = 72

Substituting in equation 2,