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

Two trains of lengths 105 m and 75 m run on parallel lines of rails. While travelling in opposite directions, they pass each other in 18 seconds. When they are running in the same direction at the same speed as before, the faster train passes the other in 36 seconds. Find the speed of the trains in km per hour.

  1. 17 km/hr, 31 km/hr

  2. 9 km/hr, 27 km/hr

  3. 21 km/hr, 36 km/hr

  4. 5 km/hr, 20 km/hr

  5. 15 km/hr, 25 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be u and v (m/s). (105+75)/(u+v) = 18 => u+v = 10. (105+75)/(u-v) = 36 => u-v = 5. Solving, u = 7.5 m/s, v = 2.5 m/s. Converting to km/hr: 7.5 * 3.6 = 27, 2.5 * 3.6 = 9.

Multiple choice

Directions: In this question, you have to find out which of the following statements is/are sufficient for determining the answer of the given question. What is the speed of the train? I. The train crosses another train in the same direction in 50 seconds. II. The train crosses a tree in 22 seconds. III. The train crosses a platform of length 380 metres in 42 seconds.

  1. Only I and II

  2. Only II and III

  3. Only II and either I or III

  4. Either II or III

  5. All I, II and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let L be length of train and V be speed. II: L/V = 22. III: (L+380)/V = 42. From II, L = 22V. Substitute into III: (22V + 380)/V = 42 => 22V + 380 = 42V => 20V = 380 => V = 19 m/s. Statement I is not needed.

Multiple choice

A train 600 m long is running at the speed of 84 km/hr. If it crosses a tunnel in 2 min, then the length of the tunnel (in m) is

  1. 2600 m

  2. 2200 m

  3. 2626 m

  4. 2400 m

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

First, convert the speed of the train from km/hr to m/s, which gives 84 * (5/18) = 70/3 m/s. In 2 minutes (120 seconds), the total distance covered by the train is (70/3) * 120 = 2800 meters. Since this total distance is the sum of the train's length and the tunnel's length, the tunnel's length is 2800 - 600 = 2200 meters.

Multiple choice

How much time does a 50 m long train, moving with a speed of 68 km/hr, take to pass another train, 75 m long moving with a speed of 50 km/hr, in the same direction?

  1. 30 sec

  2. 25 sec

  3. 32 sec

  4. 5 sec

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

When two trains move in the same direction, their relative speed is the difference of their speeds, which is 68 - 50 = 18 km/hr, or 5 m/s. The total distance to be covered to pass each other is the sum of their lengths, 50 + 75 = 125 m. The time taken is therefore 125 / 5 = 25 seconds.

Multiple choice

Two trains of lengths 580 m and 620 m are running on parallel lines. The speed of the first train is 70 kmph and the speed of the second train is 74 kmph. How long will they take to cross each other if they are moving in opposite directions?

  1. 50 seconds

  2. 30 seconds

  3. 26 seconds

  4. 45 seconds

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

The relative speed of the trains moving in opposite directions is 70 + 74 = 144 km/hr. Converting to m/s: 144 * (5/18) = 40 m/s. The total distance to cover is 580 + 620 = 1200 m. Time = distance / speed = 1200 / 40 = 30 seconds.

Multiple choice

Two trains I and II are running at speeds of 72 km/hr and 90 km/hr, respectively, on parallel tracks. When running in opposite directions, they pass each other in 10 seconds. When running in the same direction, a person sitting in the faster train (II) finds that he passes the other train (I) in 30 seconds. Find the lengths of the trains.

  1. Train I - 150 m, Train II - 300 m

  2. Train I - 250 m, Train II - 200 m

  3. Train I - 100 m, Train II - 350 m

  4. Train I - 150 m, Train II - 150 m

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

Let L1 and L2 be the lengths of the trains. The relative speed in opposite directions is 72+90 = 162 km/hr = 45 m/s, so L1+L2 = 45 * 10 = 450 m. In the same direction, the relative speed is 90-72 = 18 km/hr = 5 m/s, so L1 = 5 * 30 = 150 m. Thus, L2 = 450 - 150 = 300 m.

Multiple choice

An engineer travels 600 km to his home, partly by train and partly by car. He takes 8 hours if he travels 120 km by train and the rest by car. He takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speeds of the train and the car.

  1. 60 km/hr; 80 km/hr

  2. 30 km/hr; 40 km/hr

  3. 40 km/hr; 20 km/hr

  4. 20 km/hr; 40 km/hr

  5. 60 km/hr; 60 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let train speed be T, car speed be C. 120/T + 480/C = 8. 200/T + 400/C = 8 + 1/3 = 25/3. Solving this system: 1/T = 1/60, 1/C = 1/80. T = 60, C = 80.