CAT Practice : Speed Time, Races

You need to know the speed of Train B and apply relative speed - distance - time formula!

Crossing and overtaking trains

    Q.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

 

  • Correct Answer
    Choice D. 310 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 meters



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Visit Piverb.com
Visit Wizako.com

More questions from Speed Time, Races

  1. Speed Time - Races
  2. Speed Time - Geometry
  3. Speed Time - Cars
  4. Speed Time - Races
  5. Speed Change
  6. Speed Time - Meeting point
  7. Speed Time - Races
  8. Relative Speed
  9. Speed Time - Races
  10. Boats and Streams
  11. Relative Speed
"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi