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

Two trains each having a length of 160 metres moving in opposite directions crossed each other in 9 seconds. If one train crossed a 200-metre-long platform in 18 seconds, then the ratio of their speeds is:

  1. 2 : 3

  2. 9 : 7

  3. 5 : 8

  4. 3 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = (160+160)/9 = 320/9 m/s. Train 1 speed: (160+200)/18 = 360/18 = 20 m/s. Train 2 speed = 320/9 - 20 = 140/9 m/s. Ratio = 20 : 140/9 = 180/9 : 140/9 = 180:140 = 9:7.

Multiple choice

Two trains are moving in the same directions on a parallel track at the speed of 42 km/hr and 60 km/hr. The first train passes a man standing on a platform in 6 sec while the second train passes the man in 9 sec. In what time do the trains cross each other?

  1. 43 sec

  2. 44 sec

  3. 46 sec

  4. 48 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train 1 speed = 42 km/h = 42 * 5/18 = 35/3 m/s. Length 1 = (35/3) * 6 = 70 m. Train 2 speed = 60 km/h = 60 * 5/18 = 50/3 m/s. Length 2 = (50/3) * 9 = 150 m. Relative speed = 60 - 42 = 18 km/h = 5 m/s. Time to cross = (70 + 150) / 5 = 220 / 5 = 44 sec.

Multiple choice

Two trains leave the same station at different times and run in the same direction on parallel tracks. Train A leaves at 9 a.m. and runs at an average speed of 60 kilometers per hour. Train B leaves two hours later and runs at an average speed of 75 kilometers per hour. At what time will Train B overtake Train A?

  1. 2 p.m

  2. 5 p.m

  3. 6 p.m

  4. 7 p.m

  5. 9 p.m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Train A has a 2-hour head start, covering 120 km. The relative speed is 75 - 60 = 15 km/h. Time to overtake is 120 / 15 = 8 hours after Train B starts. Since Train B starts at 11 a.m., it overtakes at 7 p.m.

Multiple choice

A person, standing on a railway platform, noticed that a train took 21 seconds to completely cross the platform which is 84 m long, and it took 9 seconds in crossing it. The speed of the train is ______.

  1. 25.2 km/hr

  2. 32.4 km/hr

  3. 50.4 km/hr

  4. 75.64 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The train takes 21 seconds to cross the platform (length 84m) and 9 seconds to cross a point (the person). Let L be the length of the train and V be the speed. L/V = 9, so L = 9V. (L + 84)/V = 21. Substituting L: (9V + 84)/V = 21, so 9V + 84 = 21V, 12V = 84, V = 7 m/s. Converting to km/hr: 7 * 18/5 = 25.2 km/hr.

Multiple choice

The length of two trains is 240 m each. They cross a check post in 20 s and 30 s. If they travel in opposite directions towards each other, the time taken to cross each other is

  1. 12 s

  2. 16 s

  3. 20 s

  4. 24 s

  5. 28 s
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The speed of the first train is 240/20 = 12 m/s, and the second is 240/30 = 8 m/s. When moving in opposite directions, their relative speed is 12 + 8 = 20 m/s. The total distance to cover is 240 + 240 = 480 m, so time = 480 / 20 = 24 seconds.

Multiple choice

Two trains A and B having the lengths 195 m and 165 m, respectively, are running in the same direction on parallel lines. If the speed of A and B be 77 km/h and 85 km/h, respectively, what will be the time (in seconds) taken by them to cross each other?

  1. 162

  2. 164

  3. 160

  4. 166
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 85 - 77 = 8 km/h = 8 * (5/18) m/s = 40/18 = 20/9 m/s. Total distance = 195 + 165 = 360 m. Time = 360 / (20/9) = 360 * 9 / 20 = 18 * 9 = 162 seconds.

Multiple choice

A 1 km long goods train is running at a speed of 45 km/h. The time taken by this goods train to pass through a 2 km long tunnel is:

  1. 1 minute

  2. 2 minutes

  3. 3 minutes

  4. 4 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total distance to be covered is the length of the train plus the length of the tunnel, which is 1 km + 2 km = 3 km. At a speed of 45 km/h, the time taken is distance divided by speed, which is 3/45 hours. Converting this to minutes gives (3/45) * 60 = 4 minutes.

Multiple choice

Travelling along parallel paths in a railway track, two goods trains cross each other. The faster train, having a length of 180 metres, crosses a lamp post within a 15-second interval. Additionally, the slower train, with a speed 4 km/hr less than the faster one, crosses paths with the faster train in an 18-second interval. What is the length of the slower goods train, in meters?

  1. 192

  2. 215

  3. 232

  4. 225

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Faster train speed v = 180/15 = 12 m/s (43.2 km/hr). Slower train speed = 43.2 - 4 = 39.2 km/hr = 10.88 m/s. Relative speed = 12 + 10.88 = 22.88 m/s. Total distance = (L1 + L2) = 22.88 * 18 = 411.84. L2 = 411.84 - 180 = 231.84, which rounds to 232.

Multiple choice

Two persons are walking beside a railway track at respective speeds of 2 km and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

  1. 87

  2. 82

  3. 75

  4. 78
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed of the train in km/h and L be its length. The relative speeds are (v-2) and (v-4) km/h. Converting to m/s, we have L = (v-2)(5/18)*90 and L = (v-4)(5/18)*100. Equating these gives 90(v-2) = 100(v-4), so 9v - 18 = 10v - 40, meaning v = 22 km/h. Substituting back, L = 20 * (5/18) * 90 = 500 meters. Time to cross a post is L/v = 500 / (22 * 5/18) = 500 * 18 / 110 = 900/11 = 81.8 seconds, which is nearest to 82.