A train A passes a platform 250 meter long in 26 sec. Another train B passes the platform at 20 sec. And train A is 90 meter longer than train B and speed of train B is 3 meter per second more than train
A. Find the Length of train B

ATQ, Let speed of train A = vA m/s speed of train B = vB m/s length of train A = LA m length of train B = LB m Platform length = 250 m Train A passes platform in 26 s: (LA + 250) / vA = 26 ⇒ LA + 250 = 26 vA ...(1) Train B passes platform in 20 s: (LB + 250) / vB = 20 ⇒ LB + 250 = 20 vB ...(2) Given: Train A is 90 m longer than train B LA = LB + 90 ...(3) Speed of B is 3 m/s more than speed of A vB = vA + 3 ...(4) From (3): LA − LB = 90 Subtract (2) from (1): (LA + 250) − (LB + 250) = 26 vA − 20 vB LA − LB = 26 vA − 20 vB So: 90 = 26 vA − 20 vB ...(5) Substitute vB = vA + 3 in (5): 90 = 26 vA − 20 (vA + 3) 90 = 26 vA − 20 vA − 60 90 = 6 vA − 60 6 vA = 150 vA = 25 m/s From (1): LA + 250 = 26 × 25 = 650 LA = 650 − 250 = 400 m From (3): LB = LA − 90 = 400 − 90 = 310 m Answer: Length of train B = 310 m.