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

Train A is running at a speed of 36 km/hr and crosses a man who is running at a speed of 6 km/hr in the same direction as the train in 6 sec. Another train B of length 490 m is running at a speed of 54 km/hr in the opposite direction. Find the time taken by train A to cross train B.

  1. 45.4 sec

  2. 50 sec

  3. 21.6 sec

  4. 40 sec

  5. 65.6 sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train A speed = 10 m/s. Man speed = 1.66 m/s. Relative speed = 8.33 m/s. Length of A = 8.33 * 6 = 50 m. Total distance to cross B = 50 + 490 = 540 m. Relative speed (opposite) = 10 + 15 = 25 m/s. Time = 540 / 25 = 21.6 sec.

Multiple choice

A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.

  1. 3 AM next day

  2. 4 AM next day

  3. 8 AM next day

  4. 11 PM the same day
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: Answer the question independently. A train of length 220 m is travelling with a constant speed of 90 km/hr. At time t = 0, a bird flies at a constant speed of 108 km/hr from the front end of the train to its rear end and after reaching the rear end of the train immediately flies back and reaches the front end at time t = T seconds. The train advanced by 'y' m during this period. What is the value of 'y'?

  1. 1200

  2. 1000

  3. 1500

  4. 1600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative speed of the bird to the train is 108 - 90 = 18 km/hr (5 m/s) when going to the rear, and 108 + 90 = 198 km/hr (55 m/s) when returning. Time to reach the rear is 220 / 5 = 44 seconds. In 44 seconds, the train moves 90 km/hr * (44/3600) hr = 1.1 km = 1100 m. The bird is now at the rear. To return to the front, the bird must cover the train's length plus the distance the train moved. This is a relative speed problem where the bird catches up to the front. The time taken is 220 / 55 = 4 seconds. Total time T = 44 + 4 = 48 seconds. Distance train moved y = 90 km/hr * (48/3600) hr = 1.2 km = 1200 m.

Multiple choice

Directions: Answer the questions independently of each other. Two trains A and B of equal lengths i.e. 224meters are moving towards each other at a speed of 51 kmph and 57 kmph while a man is moving towards train A at a speed of 6.6kmph. What is the difference of time taken(in sec) by these two trains to cross the man.

  1. 5 sec

  2. 1 sec

  3. 2 sec

  4. 6 sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed of Train A and man = 51 + 6.6 = 57.6 kmph = 16 m/s. Time A = 224/16 = 14s. Relative speed of Train B and man = 57 - 6.6 = 50.4 kmph = 14 m/s. Time B = 224/14 = 16s. Difference = 16 - 14 = 2s.

Multiple choice

Train 𝑋 travels from Howrah to Prayagraj whereas train 𝑌 travels from Prayagraj to Howrah. Trains 𝑋 and 𝑌 leave Howrah and Prayagraj on Sunday at 5 AM and 8 AM, respectively. The trains travel on parallel track and cross each other at 20 minutes past 1 PM on the same day. If both the trains reach their destinations simultaneously at a certain time 𝑡, then 𝑡 must be

  1. 7:20 PM on Sunday

  2. 7:50 PM on Sunday

  3. 9:20 PM on Sunday

  4. 8:00 PM on Sunday
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the distance be D. Train X speed = D/T1, Train Y speed = D/T2. They meet at 1:20 PM. Train X traveled from 5 AM to 1:20 PM (8 hours 20 mins = 25/3 hours). Train Y traveled from 8 AM to 1:20 PM (5 hours 20 mins = 16/3 hours). Distance covered by X + Y = D. (D/T1)(25/3) + (D/T2)(16/3) = D. 25/3T1 + 16/3T2 = 1. If they arrive simultaneously at time t, they travel for times (t-5) and (t-8). Solving for t leads to 8:00 PM.

Multiple choice

Stations X, Y, Z, and W are situated on the same route. The distances from station X to stations Y, Z and W are 150 km, 250 km and 350 km, respectively. Trains A and B depart from X simultaneously on parallel tracks, heading towards W. At the same time, train C departs from W and travels towards X. Train C crosses train A at station Z and train B at station Y. Assuming each train maintains a constant speed, what is the ratio of the speed of train B to that of train A?

  1. 3 : 10

  2. 7 : 10

  3. 3 : 4

  4. 10 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Two trains – X and Y, start simultaneously from cities A and B travelling towards each other taking parallel routes. Exactly 8 hours later, they cross each other at city C after which, train X reduces its speed by 12 km/h and train Y increases its speed by 12 km/h, as a result of which, both reach their destinations at the same time. Had there been no changes in the speeds of the trains, considering AB = 864 km, what would have been the difference between the times when the two trains reach their destinations?

  1. 2 hours 48 minutes

  2. 3 hours 24 minutes

  3. 3 hours 36 minutes

  4. 3 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be x and y. They meet at 8 hours, so 8(x+y) = 864, meaning x+y = 108. After meeting, they cover the remaining distance. The time difference is calculated based on the speed change; the total time saved/lost is 3 hours 36 minutes.

Multiple choice

Train A crosses a man standing on a platform in 10 seconds, while Train B crosses the same man in 15 seconds .If the length of Train A is 120 meters and the length of Train B is 150 meters, then how much time (approximately) will both trains take to completely cross each other when they are moving in opposite directions?

  1. 6 seconds

  2. 8 seconds

  3. 10 seconds

  4. 12 seconds

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

Speed A = 120/10 = 12 m/s. Speed B = 150/15 = 10 m/s. Relative speed (opposite directions) = 12 + 10 = 22 m/s. Total distance = 120 + 150 = 270 m. Time = 270 / 22 = 12.27 seconds. Approximately 12 seconds.

Multiple choice

A train of length 400 m takes 15 seconds to cross a train of length 300 m traveling at 60 km per hour from the opposite direction along a parallel track. What is the speed of the longer train, in km per hour?

  1. 108

  2. 102

  3. 98

  4. 96

  5. Can no be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = (400+300)m / 15s = 700/15 m/s = 140/3 m/s. Convert to km/h: (140/3) * (18/5) = 168 km/h. Since they are in opposite directions, Relative speed = Speed1 + Speed2. 168 = Speed1 + 60. Speed1 = 108 km/h.