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 of length 120 metres overtakes another train of length 100 metres in 8 seconds. If the speed of the slower train is 27 kmph, what is the speed of the faster train?

  1. 118 kmph

  2. 101 kmph

  3. 127 kmph

  4. 126 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance to cover is 120 + 100 = 220 meters. Relative speed = distance / time = 220 / 8 = 27.5 m/s. Converting to km/h: 27.5 * 18/5 = 99 km/h. Since the faster train overtakes the slower one (27 km/h), the faster speed is 99 + 27 = 126 km/h.

Multiple choice

A train, 100 m long, moving at a speed of 50 km/hr crosses another train, 120 m long, coming from the opposite direction in 6 seconds. The speed of the second train is

  1. 132 km/hr

  2. 82 km/hr

  3. 60 km/hr

  4. 50 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = (100 + 120)m / 6s = 220/6 m/s = 110/3 m/s. Convert to km/hr: (110/3) * (18/5) = 132 km/hr. Since they are moving in opposite directions, relative speed = v1 + v2. 50 + v2 = 132 => v2 = 82.

Multiple choice

A man on a platform notices that a train going in one direction takes 10 seconds to pass him and another train of same length going in the other direction takes 15 seconds to pass him. If the length of the trains is 200 metres each, then what is the time taken by the two trains to pass one another?

  1. 8 seconds

  2. 9 seconds

  3. 11 seconds

  4. 12 seconds

  5. 15 seconds
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed of train 1 = 200m / 10s = 20 m/s. Speed of train 2 = 200m / 15s = 13.33 m/s. When passing each other, the relative speed is 20 + 13.33 = 33.33 m/s. The total distance to cover is 200 + 200 = 400m. Time = 400 / 33.33 = 12 seconds.

Multiple choice

A train is running at a speed of 48 km/hr. A passenger counts the telephone posts along the line as he passes them. If the posts are 50 m apart, then how many posts will he cross per minute?

  1. 16

  2. 20

  3. 24

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed = 48 km/hr = 48000 m / 60 min = 800 m/min. Posts are 50m apart. Number of gaps = 800/50 = 16. Number of posts = 16 + 1 = 17. However, usually, in such problems, we count the intervals or the question implies 16.

Multiple choice

Two trains running in opposite directions cross a stationary man on the platform in 72 seconds and 48 seconds, respectively. The time taken by the trains to cross each other completely is 60 seconds. What is the respective ratio of their speeds?

  1. 9 : 1

  2. 3 : 2

  3. 2 : 3

  4. 1 : 1

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

Let speeds be v1 and v2. Lengths are L1 = 72v1 and L2 = 48v2. Time to cross each other is (L1 + L2) / (v1 + v2) = 60. Substituting: (72v1 + 48v2) / (v1 + v2) = 60. 72v1 + 48v2 = 60v1 + 60v2. 12v1 = 12v2, so v1/v2 = 1/1.

Multiple choice

Two hours after a goods train passed a station, another train travelling at a speed of 63 km/hr following that goods train passed through that station. If after passing the station, the train overtakes the goods train in 7 hours, what is the speed of the goods train?

  1. 58.8 km/hr

  2. 73.5 km/hr

  3. 49 km/hr

  4. 39.2 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the speed of the goods train be v. The goods train has a 2-hour head start. When the second train starts, the goods train has traveled 2v. The second train catches up in 7 hours. Relative speed is (63 - v). Distance covered by the second train in 7 hours is 63 * 7 = 441. The goods train traveled for 2 + 7 = 9 hours. So, 9v = 441, v = 49 km/hr.

Multiple choice

A train, 150 m long, passes a pole in 15 seconds. Another train of the same length and travelling in the opposite direction and the first train, pass each other in 12 seconds. The speed of the second train is

  1. 57.6 km/h

  2. 64.16 km/h

  3. 126 km/h

  4. 54 km/h

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

The speed of the first train is 150 m / 15 s = 10 m/s. When the two trains cross each other, the total distance covered is the sum of their lengths (150 + 150 = 300 m) in 12 seconds, giving a relative speed of 300 / 12 = 25 m/s. The speed of the second train is 25 - 10 = 15 m/s, which is 15 * 18/5 = 54 km/h.

Multiple choice

Directions: The following question is accompanied by statements (I), (II) and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the question. What is the length of train, if speed of train is 90 kmph? Statements: I. Train crosses bridge in 18 seconds. II. Train crosses another train of same length, coming from opposite direction, in 9 seconds. III. Length of bridge is 50 m more than the train.

  1. Statements I and III

  2. Statements I and II

  3. Statement I and either II or III

  4. All three statements

  5. None of the statements
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A train leaves Delhi at 6 am and reaches Agra at 10 am. Another train leaves Agra at 8 am and reaches Delhi at 11:30 am. At what time do the two trains cross each another?

  1. 8:30 am

  2. 8:56 am

  3. 9:26 a.m.

  4. 9 am

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Train 1 speed = D/4. Train 2 speed = D/3.5 = 2D/7. Train 1 starts at 6 AM, Train 2 at 8 AM. At 8 AM, Train 1 has traveled D/2. Remaining distance = D/2. Relative speed = D/4 + 2D/7 = (7D+8D)/28 = 15D/28. Time = (D/2) / (15D/28) = 14/15 hours = 56 minutes. 8:00 AM + 56 minutes = 8:56 AM.

Multiple choice

5 hours after a goods train passed a station, another train travelling at a speed of 70 km/hr following that goods train, passed through that station. If after passing the station the train overtakes the goods train in 9 hours then what is the speed of the goods train?

  1. 45 km/hr

  2. 54 km/hr

  3. 67.5 km/hr

  4. 36 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed of goods train be v. Goods train travels for 5 + 9 = 14 hours. Passenger train travels for 9 hours at 70 km/hr. Distance = 70 * 9 = 630 km. Goods train speed v = 630 / 14 = 45 km/hr.