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 180 m long train crosses another 270 m long train running in the opposite direction in 10.8 seconds. If the shorter train crosses a pole in 12 seconds, what is the speed of longer train?

  1. 98 km/hr

  2. 96 km/hr

  3. 90 km/hr

  4. 88 km/hr

  5. 78 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = (180+270) / 10.8 = 450 / 10.8 = 41.66 m/s. 41.66 * 18/5 = 150 km/hr. Shorter train (180m) crosses pole in 12s, so speed = 180/12 = 15 m/s = 54 km/hr. Longer train speed = 150 - 54 = 96 km/hr.

Multiple choice

Two trains of equal length, running with the speeds of 40kmph and 60 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?

  1. 8 sec.

  2. 10 sec.

  3. 12 sec.

  4. 9 sec.

  5. 6 sec.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let L be the length of each train. Total distance = 2L. Relative speed in same direction = 60 - 40 = 20 km/h = 5.55 m/s. 2L = 5.55 * 40 = 222.22 m. Relative speed in opposite direction = 60 + 40 = 100 km/h = 27.77 m/s. Time = 2L / 27.77 = 222.22 / 27.77 = 8 seconds.

Multiple choice

Find the length of the train P? Statement I – The train P cross the train Q in 6 sec when train Q is not moving. Train Q cross train R in 68 sec when both are moving same direction, speed of train R is 25m/sec. Statement II – Train P cross train R in 64 sec when both are moving same direction. Length of train Q is 140m

  1. Only Statement I alone.

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives info about P crossing Q and Q crossing R, but no info on P's length. Statement II gives P crossing R and Q's length. We need speeds and lengths of P, Q, and R. We have too many variables and not enough equations to isolate the length of P.

Multiple choice

A 280-metre-long train, travelling at a uniform speed, crosses a platform in 60 seconds and a man standing on the platform in 20 seconds. What is the length of the platform?

  1. 560 metres

  2. 420 metres

  3. 280 metres

  4. Cannot be determined

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

Speed = Length of train / Time to cross man = 280 / 20 = 14 m/s. Time to cross platform = (Length of train + Length of platform) / Speed. 60 = (280 + P) / 14. 840 = 280 + P. P = 560.

Multiple choice

If a train crosses a km-stone in 12 seconds, how long will it take to cross 91 km-stones completely if its speed is 60 km/hr?

  1. 1 hr 30 min

  2. 1 hr 30 min 12 sec

  3. 1 hr 51 min

  4. 1 hr 1 min 3 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Crossing 91 km-stones means covering the distance between the 1st and 91st stone, which is 90 intervals of 1 km each. Distance = 90 km. Time = Distance / Speed = 90 / 60 = 1.5 hours. The train also takes 12 seconds to cross the first stone (length of train). Total time = 1 hr 30 min + 12 sec.

Multiple choice

A faster train crosses a slower train of equal length in 20 seconds. If the 2 trains are running in the same direction on parallel tracks at a speed of 50 km/hr and 32 km/hr, then what is the length of each train?

  1. 50 m

  2. 64 m

  3. 70 m

  4. 77 m

  5. 82 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 50 - 32 = 18 km/hr = 18 * (5/18) = 5 m/s. Total distance = speed * time = 5 * 20 = 100 m. Since the trains have equal length, each train is 100 / 2 = 50 m.

Multiple choice

A train with 90 kmph crosses a bridge in 36 s. Another train 100 m shorter crosses the same bridge at 45 kmph. The time taken by the second train to cross the bridge will be

  1. 60 s

  2. 64 s

  3. 68 s

  4. 72 s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train 1: 90 kmph = 25 m/s. Time = 36s. Distance (Bridge + Train1) = 25 * 36 = 900m. Train 2: 45 kmph = 12.5 m/s. Length = Train1 - 100. Distance (Bridge + Train2) = Bridge + Train1 - 100 = 900 - 100 = 800m. Time = 800 / 12.5 = 64s.