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

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same directions as the train. What is the length of the train and that of the platform in meters, respectively?

  1. 210 and 140

  2. 162.5 and 187.5

  3. 245 and 130

  4. 175 and 200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Train speed = 54 km/h = 15 m/s. Man speed = 9 km/h = 2.5 m/s. Relative speed (same direction) = 15 - 2.5 = 12.5 m/s. Train length = 12.5 * 14 = 175 m. Time to cross platform = 25s. Total distance = 15 * 25 = 375 m. Platform length = 375 - 175 = 200 m.

Multiple choice

A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train? (Assume that the trains run at uniform speeds)

  1. 2 : 1

  2. 3 : 2

  3. 4 : 3

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

Let speeds be P and G. Relative speed opposite = P+G, same = P-G. Time = Distance / Speed. D/(P-G) = 3 * D/(P+G). P+G = 3P-3G => 4G = 2P => P/G = 2/1.

Multiple choice

Two trains start at the same time from two stations A and B towards each other. They arrive at B and A respectively in 5 hours and 20 hours after they passed each other. If the speed of the train that started from A is 56 kmph, then what is the speed of the second train (in kmph)?

  1. 28 kmph

  2. 26 kmph

  3. 24 kmph

  4. 22 kmph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For two objects moving towards each other, the ratio of their speeds is the square root of the inverse ratio of the times taken after meeting: v1/v2 = sqrt(t2/t1). Here, 56/v2 = sqrt(20/5) = sqrt(4) = 2. Thus, v2 = 56 / 2 = 28 kmph.

Multiple choice

The ratio of the lengths of trains Ajanta Express and Thalys is 7 : 9. Moreover, the time taken by both trains to cross a pole on the platform is in the ratio 4 : 5. If the speed of Ajanta Express is 70 km/hr, then find the speed of Thalys in m/s.

  1. 40 m/s

  2. 25 m/s

  3. 29 m/s

  4. 20 m/s

  5. 18 m/s
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the lengths be 7x and 9x, and the times be 4y and 5y. Speed = length / time. Speed of Ajanta = 7x / 4y = 70 km/hr, so x/y = 40. Speed of Thalys = 9x / 5y = (9/5) * (x/y) = (9/5) * 40 = 72 km/hr. Converting 72 km/hr to m/s gives 72 * (5/18) = 20 m/s.

Multiple choice

A train passes two persons cycling in the same direction as the train in 10 sec and 15 sec, where the speeds of the two cyclists are 9 km/hr and 18 km/hr, respectively. Find the length of the train.

  1. 74 m

  2. 73 m

  3. 75 m

  4. 70 m

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let L be the length of the train and v be its speed in m/s. Cyclist speeds: 9 km/hr = 2.5 m/s, 18 km/hr = 5 m/s. Relative speeds: (v - 2.5) and (v - 5). L = 10(v - 2.5) and L = 15(v - 5). 10v - 25 = 15v - 75 => 5v = 50 => v = 10 m/s. L = 10(10 - 2.5) = 75 m.

Multiple choice

A 450 m long train moving with the speed of 90 km/h crosses a platform in 30 seconds. A man crosses the platform in 2 minutes. What is the speed of the man?

  1. 1.5 m/s

  2. 4 m/s

  3. 2.5 m/s

  4. 6 m/s

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, convert the train's speed to m/s: 90 * 5/18 = 25 m/s. In 30 seconds, the train travels 25 * 30 = 750 m, which is the sum of the train's length and the platform's length, meaning the platform is 750 - 450 = 300 m long. Since the man crosses this 300 m platform in 2 minutes (120 seconds), his speed is 300 / 120 = 2.5 m/s.

Multiple choice

A train passes an electric pole in 10 seconds and a platform that is 130 m long in 20 seconds. What is the length of the train?

  1. 130 m

  2. 140 m

  3. 150 m

  4. 160 m

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let L be the length of the train and v be its speed. The train covers its own length in 10 seconds (L = 10v) and its length plus the platform in 20 seconds (L + 130 = 20v). Substituting L = 10v into the second equation gives 10v + 130 = 20v, so 10v = 130, meaning L = 130 m.