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.  Choose the correct choice from the following:
A) 400 m	B) 810 m	C) 500 m	D) 310 m	E) 210 m
DETAILED SOLUTION   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   CORRECT ANSWER 310 m
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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.