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 P, whose length is 328 m can cross a 354 m long platform in 22 seconds. Train Q can cross the same platform in 24 seconds. If the speed of train Q is (\frac{7}{8})th of the speed of train P, what is the length (in meter) of train Q?

  1. 321

  2. 303

  3. 297

  4. 273

  5. 309
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train P: Speed = (328 + 354)/22 = 682/22 = 31 m/s. Train Q speed = (7/8) × 31 = 27.125 m/s. Let Q's length be L: (L + 354)/24 = 27.125, so L + 354 = 651, giving L = 297 m. Answer C is correct.

Multiple choice

Train A of length 140 m can cross a platform of length 180 m in 16 seconds and the ratio of speed of train B and train A is 3: 2. Find the length of train B if train B crosses a man in 15 seconds.

  1. 350 m

  2. 450 m

  3. 295 m

  4. 300 m

  5. 360 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train A speed: (140 + 180)/16 = 320/16 = 20 m/s. Train B speed: (3/2) × 20 = 30 m/s. Train B crosses a man (stationary object) in 15 seconds, so its length = 30 × 15 = 450 m. Option B is correct.

Multiple choice

Two trains are running with speed 30 km/hr. and 58 km/hr. in the same directions. A man in the slower train passes by the faster train in 18 seconds. The length (in metres) of the faster train is:

  1. 120

  2. 130

  3. 140

  4. 125

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

Relative speed when trains move in same direction = 58-30=28 km/hr = 28×(5/18)=70/9 m/s. In 18 seconds, the distance covered (length of faster train) = (70/9)×18=140 meters. The man in the slower train observes the faster train passing by completely.

Multiple choice

Two trains are running on parallel tracks whose lengths are 100 meters and 80 meters respectively. If they travel in the same direction, they cross each other in 18 seconds. If they travel in the opposite direction, they cross each other in 9 seconds. Find the speed of the faster moving train?

  1. 15

  2. 5

  3. 20

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be x (faster) and y (slower) in m/s. Same direction: relative speed = (x-y), distance = 180m, so x-y = 180/18 = 10. Opposite direction: relative speed = (x+y), so x+y = 180/9 = 20. Solving: adding gives 2x = 30, so x = 15 m/s. Option A (15) is correct.

Multiple choice

Two trains running in the same direction if the faster train crosses the slower train in 48 seconds while in opposite direction they cross each other in 12 seconds if the speed of the faster train 105 km/hr .Find the speed of the slower train.

  1. 83 km/hr

  2. 56 km/hr

  3. 63 km/hr

  4. 78 km/hr

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

Let slower train speed = x kmph. Same direction: relative speed = (105-x) kmph, time 48s = 48/3600 hr. Distance = (105-x)×48/3600. Opposite direction: relative speed = (105+x) kmph, time 12s. Distance = (105+x)×12/3600. Equating: (105-x)×48 = (105+x)×12. Solving: 5040-48x = 1260+12x → 3780 = 60x → x = 63 kmph.

Multiple choice

A 248 m long train running at a speed of 108 km/h overtook another train of length 112 m in 36 seconds. What is the speed of the other train?

  1. 66km/hr

  2. 70km/hr

  3. 72km/hr

  4. 75km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When one train overtakes another, the relative speed is the difference of their speeds. Total distance covered is sum of both train lengths (248+112=360m). Relative speed = 360/36 = 10 m/s = 36 km/h. Speed of other train = 108-36 = 72 km/h.

Multiple choice

A train can cross a man running in the same direction in 10 seconds. If the speed of the man is 5 m/s and the length of the train is 200 m, then find the speed (in m/s) of the train?

  1. 25

  2. 30

  3. 35

  4. 40

  5. 45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed of train with respect to man = (speed of train - 5) m/s. Distance covered = length of train = 200 m. Time = 10 seconds. So 200/(speed - 5) = 10, which gives speed - 5 = 20, therefore train speed = 25 m/s.

Multiple choice

A train covered a certain distance at a uniform speed. If the train had been 6 km/h faster, then it would have taken 8 hours less than the scheduled time. And, if the train were slower by 6 km/h, then the train would have taken 12 hours more than the scheduled time. 140% of the length of the journey is

  1. 2000 km

  2. 2012 km

  3. 2014 km

  4. 2016 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the original speed be v km/h and distance be D km. Original time = D/v. With speed (v+6): time = D/(v+6) = D/v - 8. With speed (v-6): time = D/(v-6) = D/v + 12. This gives us two equations: D/(v+6) = D/v - 8 and D/(v-6) = D/v + 12. Solving this system gives v = 30 km/h and D = 1440 km. 140% of D = 1.4 × 1440 = 2016 km.

Multiple choice

The following question has some statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. How much time will train A take to cross another train B running in opposite direction? Statement 1: Train A crosses a pole in 7 seconds. Statement 2: Ratio of speed of trains A and B is 3:5 Statement 3: length of two trains together is 500m.

  1. Statement 1 and 2 together

  2. All statement are required

  3. Statement 2 and 1 or 3 together

  4. Only statement 1 is sufficient

  5. All statement are not sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find the time for train A to cross train B, we need the formula: time = (length of A + length of B) / (speed of A + speed of B). Statement 1 gives the relationship between length and speed of A only. Statement 2 gives only the ratio of speeds, not actual values. Statement 3 gives combined length but not individual lengths. None of these provide absolute values or complete information needed.