Train A requires 15 seconds to cross train B of length 300 m moving in the opposite direction at a speed of 36 km/h. Further, train A requires 30 seconds to cross a 500 m long stationary train C. Find the length (in m) of train A.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 200.
When two objects are moving in opposite direction (coming towards each other) then
Relative speed = S1 + S2
Where S1 = speed of object 1
S2 = speed of object 2
Let the length of train A = LA
Speed of train A = SA
Speed of train B (in m/s) = 36 × 5/18 = 10 m/s
According to the question;
When train A cross, train B moving in opposite direction;
⇒ (LA + 300)/15 = 10 + SA
⇒ LA + 300 = 150 + 15SA ----- (1)
Now, when train A cross, train C
⇒ (LA + 500)/30 = SA
⇒ (LA + 500) = 30SA
We can write the above equation as;
⇒ LA + 300 + 200 = 30SA ----- (2)
Using equation (1) in (2), we get
⇒ 150 + 15SA + 200 = 30SA
⇒ SA = 350/15 ----- (3)
Now using equation (3) in (1), we get
⇒ (LA + 500)/30 = 350/15
⇒ LA + 500 = 700
⇒ LA = 200