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 450 meter long train crosses a bridge 650 meters long in 36 seconds. What is speed (in km/hr) of the train? 450 मीटर लंबी ट्रेन 36 सेकंड में 650 मीटर लंबा एक पुल पार करती है। ट्रेन की गति (किमी / घंटा में) क्या है?

  1. 110

  2. 125

  3. 150

  4. 95
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = length of train + length of bridge = 450 + 650 = 1100 m. Time = 36 seconds. Speed = 1100/36 = 30.56 m/s = 30.56 × 18/5 = 110 km/hr. When a train crosses a bridge/pole, add their lengths to get total distance covered.

Multiple choice

A train crosses a platform in 50 seconds travelling with a speed of 72 km/hr. If the length of the train be 250 metres, then what will be the length (in metres) of the platform? एक ट्रेन 72 किमी / घंटा की गति से यात्रा करते हुए 50 सेकंड में एक प्लेटफ़ॉर्म पार करती है। यदि ट्रेन की लंबाई 250 मीटर है, तो प्लेटफॉर्म की लंबाई (मीटर में) क्या होगी?

  1. 600

  2. 480

  3. 750

  4. 950
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed = 72 km/hr = 72 × 5/18 = 20 m/s. Distance covered in 50 seconds = 20 × 50 = 1000m. This distance equals train length + platform length. Therefore platform length = 1000 - 250 = 750m.

Multiple choice

A train 150 m. long is running with a speed of 68 km. /hr. In what time will it pass a man who is running at 8 km. /hr. in the same direction in which the train is going? एक 150 मी. लम्बी ट्रेन 68 किमी./घं. की चाल से चल रही है। कितने समय में एक आदमी को पार करेगी जो उसी दिशा में 8 किमी./घं. की चाल से जा रहा है, जिधर ट्रेन जा रही है?

  1. 7 seconds/सेकेण्ड

  2. 9 seconds/सेकेण्ड

  3. 12 seconds/सेकेण्ड

  4. 8 seconds/सेकेण्ड
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When objects move in the same direction, subtract their speeds to get relative speed: 68 - 8 = 60 km/hr. Convert to m/s: 60 × 5/18 = 50/3 m/s. Time = Distance/Speed = 150 ÷ 50/3 = 150 × 3/50 = 9 seconds. Option A (7s) and D (8s) are calculation errors. Option C (12s) would result from adding speeds instead of subtracting.

Multiple choice

What is the length of the slower train? I. The faster train of length 100 m takes 10 seconds to pass a man sitting in the slower train. II. The speed of the faster train is 80 km/hr.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If both statement together are sufficient, but neither statement alone is sufficient.

  4. If each statement alone (either I or II) is sufficient.

  5. If statement I and II together are not sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find the slower train's length, we need either its own length or speed, or the relative speed and time data. Statement I gives time (10 seconds) but not relative speed - we know the faster train's speed but not whether the slower train is moving or stationary. Statement II gives only the faster train's speed (80 km/hr). Even together, we don't know if the man is stationary or moving with the slower train, nor do we know the slower train's speed or length. The information is insufficient.

Multiple choice

Find the value of both quantities and then state the correct relationship.\nA train of length (x) meters travelling at the speed of 36 km per hour can cross a pole standing on a platform in 15 seconds but at the speed of 54 km per hour it can cross a platform of (y) meters long in 24 seconds. \nQuantity I : What is the length of the train? \nQuantity II : What is the length of the platform?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed 36 km/h = 10 m/s. In 15 seconds, train length = 10 × 15 = 150m. Speed 54 km/h = 15 m/s. In 24 seconds, train + platform = 15 × 24 = 360m. Platform length = 360 - 150 = 210m. Since 210m > 150m, Quantity II (platform) > Quantity I (train).

Multiple choice

A train left from station A for station B at 4pm at an average speed of 80 kmph. At 8 pm, another train also had left from station A for station B on a parallel track at an average speed of 120 kmph. How far from A is another train expected to overtake the first train?

  1. 750

  2. 840

  3. 960

  4. 920

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

First train travels for 4 hours (4pm to 8pm) at 80 kmph, covering 320 km. Second train starts at 8pm at 120 kmph. Relative speed = 120 - 80 = 40 kmph. Time to catch up = 320/40 = 8 hours. Distance from A = 120 × 8 = 960 km. The second train overtakes the first at 960 km from station A.

Multiple choice

Two trains of same length take 60 seconds and 90 seconds, respectively to cross a pole. If both the trains are running in the same direction, then how long will they take to cross each other?

  1. 300 seconds

  2. 360 seconds

  3. 400 seconds

  4. 420 seconds
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let L be the length of each train. Speed of first train = L/60 (m/s). Speed of second train = L/90 (m/s). When moving in the same direction, relative speed = L/60 - L/90 = L/180 (m/s). To cross each other, they must cover the combined distance of 2L. Time = Distance/Speed = 2L ÷ (L/180) = 2L × 180/L = 360 seconds. This is a standard relative speed problem where trains of equal length cross each other moving in the same direction. Option B (360 seconds) is correct.

Multiple choice

A train of length x meters travelling at the speed of 54 km per hour can cross a boy standing on a platform in 16 seconds but at the speed of 72 km per hour it can cross a platform of y meters long in 24 seconds. Quantity I: What is the length of the train? Quantity II: What is the length of the platform?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

From statement 1: x / (54×5/18) = 16, so x = 240m (train length). From statement 2: (x+y) / (72×5/18) = 24, so x+y = 240m. Since x = 240m, y = 0m which is unrealistic. Both quantities equal 240m, so relation is 'equal'.

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly. What is the speed of the train? Statement I: The train crosses 300 metres long platform in 45 seconds. Statement II: The train crosses another stationary train of same length in 60 seconds. Statement III: The train crosses a signal pole in 30 seconds.

  1. Only III and I or II

  2. Any two of the three

  3. Only II and I or III

  4. Only I and II

  5. Only I and II or III
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let L be train length, S be speed. From I: L+300 = 45S. From II: 2L = 60S, so L = 30S. From III: L = 30S. Substituting L=30S in I: 30S + 300 = 45S, so 15S = 300, S = 20 m/s. We need two statements: either I and II (gives L and S), or I and III (same as II), or II and III (both give L=30S, need one more). So 'Only I and II or III' means we need statement I plus either II or III.

Multiple choice

A train running at the speed of (15\frac{m}{s}) takes 20 seconds to pass a man running at the speed of (5\frac{m}{s}) in the same direction. Find the length of the train.

  1. 100 meters

  2. 200 meters

  3. 250 meters

  4. 400 meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When two objects move in the same direction, their relative speed is the difference of their individual speeds. Relative speed = 15 - 5 = 10 m/s. Distance covered in 20 seconds = 10 × 20 = 200 meters. This distance equals the length of the train.

Multiple choice

If the speed of the train be 80 kmph and it takes 18 seconds to cross a platform. Next it takes 5 seconds to cross a cyclist cycling at the rate of 8 km/hr. in the same direction. What is the length of the platform?

  1. 200 m

  2. 300 m

  3. 100 m

  4. 400 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convert speed to m/s: 80 kmph = 80 × 5/18 = 22 2/9 m/s. Cyclist speed = 8 × 5/18 = 20/9 m/s. Relative speed (same direction) = 22 2/9 - 20/9 = 180/9 = 20 m/s. Length of train = 20 × 5 = 100 m. Distance covered crossing platform = 22 2/9 × 18 = 400 m. Platform length = 400 - 100 = 300 m. Option B is correct.

Multiple choice

Two trains, each of length 125 metre, are running in parallel tracks in opposite directions. One train is running at a speed 65 km/hr. and they cross each other in 6 seconds. The speed of the other train is -

  1. 75 km/hr.

  2. 85 km/hr.

  3. 95 km/hr.

  4. 105 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance to cross = sum of lengths = 125 + 125 = 250 m = 0.25 km. Time = 6 seconds = 6/3600 hours. Relative speed = Distance / Time = 0.25 / (6/3600) = 0.25 × 3600 / 6 = 150 km/hr. Since trains move in opposite directions, relative speed = v1 + v2. So v2 = 150 - 65 = 85 km/hr. Option B is correct.

Multiple choice

A train X travelling at 72 km/h crosses another train Y travelling at 63 kmph in opposite direction in 18 seconds. If the length of train Y is two third the length of the X, then find the length of the X?

  1. 405

  2. 550

  3. 475

  4. 425
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Trains X and Y move in opposite directions, so relative speed = 72 + 63 = 135 km/h = 135 × 5/18 = 37.5 m/s. Distance covered in 18 seconds = 37.5 × 18 = 675 m = sum of both train lengths. Let Lx be length of X, then Ly = (2/3)Lx. So Lx + (2/3)Lx = 675, (5/3)Lx = 675, Lx = 405 m. The key concepts are converting relative speed to m/s and understanding that crossing time depends on combined lengths.

Multiple choice

A train crosses a 600 meter long platform in 50 seconds. It crosses another 900 metre long platform in 60 seconds. What are the length and speed of the train?

  1. 900 metres, 96 km/h

  2. 900 metres, 108 km/h

  3. 600 metres, 108 km/h

  4. 700 metres, 108 km/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let L = train length, S = speed. From first platform: L + 600 = S × 50. From second platform: L + 900 = S × 60. Subtracting gives 300 = 10S, so S = 30 m/s = 30 × 18/5 = 108 km/h. Substituting: L = 30 × 50 - 600 = 1500 - 600 = 900m. Verify: Option B gives length 900m, speed 108 km/h (30 m/s). Cross-check: 900+600=1500m at 30 m/s takes 50 seconds ✓; 900+900=1800m takes 60 seconds ✓