The question is from the topic relative speed. It discusses about crossing and overtaking trains. Speed of one train and time taken to cross is given, we need to find out the lenth of the train. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 13: 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

310 m

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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."**

Choice D is the correct answer.

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