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

Which information are necessary to answer the questions asked- What is the length of the train X? I. Two trains X and Y running in opposite directions and cross each other in 25 seconds. II. The length of the train Y is 320m and the difference between the speeds of trains X and Y is 14 km/h. III. The ratio of the speed of the trains is 19:26.

  1. Only II and III

  2. Only I and III

  3. Any two

  4. All three together are not sufficient

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

Using all three statements: Speeds are in ratio 19:26, let them be 19k and 26k km/h. Speed difference = 7k = 14, so k=2. Speeds: 38 km/h and 52 km/h. Relative speed in opposite direction = 90 km/h = 25 m/s. Crossing time 25s = (Lx + 320)/25, so Lx = 25×25 - 320 = 625-320 = 305m. All three together ARE sufficient, but options A-D are incorrect. E is correct as 'None of these'.

Multiple choice

A train moves past a metal board in 20 sec and a station 300 m long in 50 sec. Its length and speed are:

  1. 100 m, 20 m/sec

  2. 200 m, 10m/sec

  3. 105 m, 10m/sec

  4. 200 m, 20 m/sec

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let train length = L and speed = S. When passing a metal board (considered a point), time = L/S = 20 seconds, so L = 20S. When passing a 300m station, time = (L+300)/S = 50 seconds. Substituting L = 20S: 20S + 300 = 50S, which gives 300 = 30S, so S = 10 m/s and L = 200m.

Multiple choice

A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of x (in m)?

  1. 200

  2. 168

  3. 210

  4. 252
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = 74 + 52 = 126 km/h = 35 m/s. In 12 seconds, total distance covered = 35 × 12 = 420 m (sum of both train lengths). If L is length of x, then length of y = (2/3)L. So L + (2/3)L = 420, giving (5/3)L = 420, so L = 420 × 3/5 = 252 m.

Multiple choice

Two trains are running in the same direction at the speed of 50 km./hr. and 30 km./hr. respectively. The faster train crosses a man in the slower train in 18 seconds. What is the length of the faster train ?

  1. 0.1 km.

  2. 1 km.

  3. 1.5 km.

  4. 1.4 km.

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

Relative speed = 50 - 30 = 20 km/hr = 20 × 5/18 = 50/9 m/s. Distance (length of faster train) = Relative speed × Time = (50/9) × 18 = 100 meters = 0.1 km. Option A is correct. The other options are too large.

Multiple choice

There are two trains of same lengths one take 20 seconds and 30 seconds respectively to cross a telegraph post. Trains are travelling in opposite direction if the length of each train be 150 metres.In what time (in seconds) will they cross each other?

  1. 30 sec.

  2. 24 sec.

  3. 40 sec.

  4. 20 sec.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first train's speed is 150/20 = 7.5 m/s, and the second's is 150/30 = 5 m/s. When traveling in opposite directions, their relative speed is the sum: 7.5 + 5 = 12.5 m/s. To cross each other, they must cover the total distance of both trains (150 + 150 = 300m). Time = distance/speed = 300/12.5 = 24 seconds.

Multiple choice

A train of speed 40 km/hr is moving in the same direction of a horse moving at the speed of 25 km/hr crosses in 48 sec. Find the length of train?

  1. 400 meter

  2. 500 meter

  3. 300 meter

  4. 250 meter

  5. 200 meter
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

When two objects move in the same direction, their relative speed is the difference of their individual speeds. Relative speed = 40 - 25 = 15 km/hr. Converting to m/s: 15 × (5/18) = 25/6 m/s. Length of train = relative speed × time = (25/6) × 48 = 200 meters. Option E is correct.

Multiple choice

Train ‘A’ running at speed of 54 km/hr crosses a platform of length same as that of the train in 36 sec. If train B, which is 250 meters long crosses the same platform in 25 sec, then find speed of train B (in km/hr)?

  1. 72.88

  2. 73.26

  3. 82.62

  4. 74.88

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

Let platform and train A length = L meters. Train A: 54 km/hr = 15 m/s. Distance = 2L, time = 36s, so 15 × 36 = 2L, L = 270m. Train B: length = 250m, crosses platform (270m) in 25s. Distance = 250 + 270 = 520m in 25s, speed = 520/25 = 20.8 m/s = 74.88 km/hr.

Multiple choice

A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in metre) ? 84 किमी/घंटा की गति से चल रही एक ट्रेन 6 किमी/घंटा की गति से विपरीत दिशा में चल रहे एक व्यक्ति को 4 सेकंड में पार कर जाती है। ट्रेन की लंबाई (मीटर में) क्या है?

  1. 100

  2. 120

  3. 80

  4. 75

  5. 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 84 + 6 = 90 km/hr (opposite directions). Convert to m/s: 90 × 5/18 = 25 m/s. Time to pass the man = 4 seconds. Length = speed × time = 25 × 4 = 100 meters.

Multiple choice

Train A completely crosses train B which is 205 m long in 16 second. If they are travelling in opposite direction and sum of speed of both are 25 m/s. then find the difference (in meter) between lengths of both trains. ट्रेन A, 205 मीटर लंबी ट्रेन B को 16 सेकंड में पूरी तरह से पार करती है। यदि वे विपरीत दिशा में यात्रा कर रहे हैं और दोनों की गति का योग 25 मीटर/सेकेंड है। तो दोनों ट्रेनों की लंबाई के बीच का अंतर (मीटर में) ज्ञात कीजिए।

  1. 20 meter 20 मीटर

  2. 10 meter 10 मीटर

  3. 15 meter 15 मीटर

  4. 5 meter 5 मीटर

  5. 25 meter 25 मीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When trains cross in opposite directions, relative speed = 25 m/s. Total distance covered = sum of lengths = L_A + 205. Time = 16 seconds, so L_A + 205 = 25 × 16 = 400. Thus L_A = 400 - 205 = 195 m. The difference = 205 - 195 = 10 m.

Multiple choice

The speed of train A and B is 126" " km/h and 288" " km/h respectively. B crosses A in 22 seconds while both are running in the same directions. If length of B is 250" " m more than A, what will be the time (in sec) taken by A to cross a platform of length 505" " m ?

  1. 26

  2. 28

  3. 20

  4. 25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed in same direction = 288 - 126 = 162 km/h = 45 m/s. In 22 seconds, B covers A + (A + 250) = 990 m, so A's length = 370 m. A crosses 505 m platform: distance = 370 + 505 = 875 m. Time = 875 ÷ 35 = 25 seconds.

Multiple choice

A train of length 80 m crosses a platform of length 280m in 2 minutes. A person who is running in opposite direction of train crosses the train in 16 seconds. What is the speed of the person?

  1. 2 m/sec

  2. 2.5 m/sec

  3. 1 m/sec

  4. 0.5 m/sec
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train crosses platform of length 280 m + its own length 80 m = 360 m in 2 minutes = 120 seconds. Train speed = 360/120 = 3 m/sec. Person running opposite direction crosses train in 16 seconds. Relative speed = train speed + person's speed = 80/16 = 5 m/sec. Person's speed = 5 - 3 = 2 m/sec.

Multiple choice

A fastmoving superfast express crosses another passenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also, the length of faster train is 100 m, then find the length of the slower train if they are moving in the same direction.

  1. 120 metres

  2. 110 metres

  3. 150 metres

  4. 160 metres

  5. 112 metres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speeds: 72 km/hr and 27 km/hr in same direction. Relative speed = 72-27 = 45 km/hr = 45×5/18 = 12.5 m/s. Time = 20 seconds. Total distance covered in 20 seconds = 12.5 × 20 = 250 m. This equals sum of both train lengths. Length of slower train = 250 - 100 = 150 m.

Multiple choice

The length of train A is twice that of train B and speed of train A is half of that of train B. If train A crosses a man in 4 sec. then find how long will train B take to cross train A if they go in same direction.

  1. 3 second

  2. 4 second

  3. 5 second

  4. 6 second

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

Let train B have length L and speed V. Then train A has length 2L and speed V/2. Train A crosses man in 4 sec: 2L = (V/2) × 4, so V = L. In same direction, relative speed = V - V/2 = V/2. Time to cross: 3L/(V/2) = 3L/(L/2) = 6 seconds.