# CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

###### CAT Questions | Time and distance | Relative Speed

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.

1. 400 m
2. 810 m
3. 500 m
4. 310 m

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##### Method of solving this CAT Question from Time Speed Distance: Relative speed in the same and opposite directions.

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

Choice D is the correct answer.

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