Quantitative Aptitude

Problems on Trains

989 Questions
All Passing a moving person or another train 430 Crossing a platform or bridge 379 Crossing a pole or stationary person 104 Meeting point and post-meeting times 52 Journey time, reduced speed, and schedule conditions 24

Problems on Trains Questions

Multiple choice

A train passes over a $400$ $\mathrm { m }$ long bridge. If the speed of thetrain is $300$$\mathrm { m } / \mathrm { s }$ and the train takes $2$ $\mathrm { s }$ to cross the bridge, find the length of the train.
  1. $400$ $\mathrm { m }$
  2. $600$  $\mathrm { m }$
  3. $800$ $\mathrm { m }$
  4. $200$ $\mathrm { m }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance = speed * time. Distance = length of train + length of bridge. (L + 400) = 300 * 2 = 600. L = 600 - 400 = 200 m.

Multiple choice

Two trains each of length L are moving on parallel tracks with constant speeds. they take 40 s to overtake each other, if same trains are made to cross each other with earlier speeds then it requires just 20 s. ratio of speeds of the two trains is

  1. 1:1

  2. 2:1

  3. 3:1

  4. 4:1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v1, v2. Overtaking: 2L / (v1-v2) = 40. Crossing: 2L / (v1+v2) = 20. Thus v1+v2 = 2(v1-v2). v1+v2 = 2v1-2v2, so v1 = 3v2. Ratio 3:1.

Multiple choice

A train moves in straight line with a uniform acceleration. If x and y be the velocities with which the front and rear end of the train respectively cross a fixed pole then the velocity with which the middle of the train crosses the pole is:
  1. $ \dfrac { x^2+y^2}{ 2 } $
  2. $ \dfrac { 2xy }{ x+y } $
  3. $ \sqrt { \dfrac { 1 }{ 2 } \left( { x }^{ 2 }+{ y }^{ 2 } \right) } $
  4. $ \sqrt { \dfrac { 1 }{ 2 } \left( { y }^{ 2 }-{ x }^{ 2 } \right) } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Two trains one of length $100\ m$ and another of length $125m$, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $10m/s$. If their acceleration are $0.3m/{s}^{2}$ and $0.2m/{s}^{2}$ respectively, then the time they take to pass each other will be
  1. $5\ s$
  2. $10\ s$
  3. $15\ s$
  4. $20\ s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative initial velocity = 10 - (-10) = 20 m/s. Relative acceleration = 0.3 - (-0.2) = 0.5 m/s^2. Total distance to cover = 100 + 125 = 225 m. Using s = ut + 0.5at^2: 225 = 20t + 0.5(0.5)t^2. 0.25t^2 + 20t - 225 = 0. t^2 + 80t - 900 = 0. (t + 90)(t - 10) = 0. t = 10.