Question

Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.
400 m
810 m
500 m
310 m

Answer 1

Answer:

Step-by-step explanation:

Let the length of Train A be x meters  

Let speed of Train B be y kmph

Relative distance = Relative speed * time taken to cross/overtake

Crossing scenario:

Relative speed of 2 trains = 63 + y  

Time taken to cross = 27 sec or 27/3600 hrs

Relative distance between 2 trains = Length of Train A + length of train B = (x + 0.5) km

Therefore, x + 0.5 = (63 + y) * 27 / 3600 ----- (1)

Overtaking scenario:

Relative speed of 2 trains = 63 – y  

Time taken to overtake = 162 sec or 162/3600 hrs

Relative distance between 2 trains = x + 0.5

Therefore, x + 0.5 = (63 – y) * 162/3600 --- (2)

From (1) and (2), solve for y.

(63 + y) * 27 = (63 – y) * 162  

27y + 162 y = 63*162 – 63 *27  

189y = 63 * 135 or y = 45 kmph

Substitute in (2) to get x.

x + 0.5 = (63 – 45) * 162/3600  

Or x = 0.31 km or 310 meters

The question is "If the length of train B is 500 meters, find the length of Train A."

Hence, the answer is 310 m

Answer 2

Answer:

310 m

Step-by-step explanation:

Let say Length of Train A = A km

Length of Train B = 500 m = 0.5 km

Let say speed of train B = B km/Hr

Distance covered in opposite directions = A + 0.5 km

Time taken = 27 sec = 27/3600 hr

63*(27/3600)  + B*(27/3600)  = A + 0.5

=> 1701 + 27B = 3600A + 1800

=> 27B = 3600A + 99   - eq 1

Let say after travelling of x km of Train B , Train A crosses

63*(162/3600)  - B*(162/3600) = A + 0.5

=> 63*(9/200)  - B*(9/200) = A + 0.5

=> 567 - 9B = 200A + 100

=> 9B = -200A + 467

Multiplying by 3

=>27B = -600A + 1401   - eq 2

Equating eq 1 * eq 2

3600A + 99 = -600A + 1401

=> 4200A = 1302

=> A = 1302/4200

=> A = 0.31

Length of Train A = 0.31 km = 310 m