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

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. Train A running at a speed of 144 km/h crosses a platform of length 200 m in 8 seconds. Train B running at a speed of 108 km/h crosses a platform of length 180 m in 10 seconds. Quantity I: Length of train A Quantity II: Length of train B

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train A: Speed = 144 * 5/18 = 40 m/s. Distance = 40 * 8 = 320m. Length = 320 - 200 = 120m. Train B: Speed = 108 * 5/18 = 30 m/s. Distance = 30 * 10 = 300m. Length = 300 - 180 = 120m. Both are 120m.

Multiple choice

Two trains A and B have lengths equal to 120 m and 24 m, respectively. Train A passes train B in 12 sec. If train B travelling in opposite direction has a speed of 4 m/sec, find the speed of the train A (in km/hr).

  1. 25.3

  2. 26 .67

  3. 28.8

  4. 30

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

Total distance = 120 + 24 = 144 m. Relative speed = 144 / 12 = 12 m/s. Since they are in opposite directions, relative speed = speed A + speed B. 12 = speed A + 4, so speed A = 8 m/s. 8 m/s = 8 * (18/5) = 28.8 km/h.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. Train A and train B are running parallel on two tracks. What is the sum of the lengths of both the trains? I. Train A crosses train B in 20 seconds. II. Length of train A is 80 m. III. Speed of train A is 36 kmph more than that of train B.

  1. Only statements I and II

  2. Only statements I and III

  3. None of the statements

  4. All three statements

  5. Any two statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the sum of the lengths (L1 + L2), we need the relative speed. Statement I gives the time taken to cross. Statement III provides the difference in speeds. We need the actual speeds or the sum of speeds to determine the distance covered (L1 + L2 = relative speed * time). Statements I and III are necessary to relate the lengths to the speeds.

Multiple choice

Directions: The question below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. What is the speed of the train? Statements: A. The train overtakes Sam in 7.5 seconds and Kunal in 8 seconds. B. Sam and John walk at the speeds of 5 km/hr and 6 km/hr, respectively. C. Sam and John are walking in the same direction as that of the train.

  1. Any two of the three

  2. Either A or B

  3. Either B or C

  4. All of the three

  5. Only C
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A train passes two persons, walking at the speeds of 2 km/hr and 4 km/hr in the same direction as the train, completely in 9 seconds and 10 seconds, respectively. Calculate the length of the train (in metres).

  1. 54

  2. 45

  3. 50

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

Let L be length and v be train speed. (v-2) * 5/18 * 9 = L and (v-4) * 5/18 * 10 = L. (v-2) * 2.5 = (v-4) * 2.777. 2.5v - 5 = 2.777v - 11.11. 0.2777v = 6.11, v = 22. L = (22-2) * 5/18 * 9 = 20 * 2.5 = 50.

Multiple choice

An express train 130 m long moving at a speed of 80 km/hr crosses a train 120 m long coming from opposite direction in 5 sec. Find the speed of the second train.

  1. 140 km/hr

  2. 130 km/hr

  3. 110 km/hr

  4. 100 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = Total distance / Time = (130 + 120) / 5 = 250 / 5 = 50 m/s. 50 m/s = 50 * 18/5 = 180 km/hr. Since they are moving in opposite directions, relative speed = v1 + v2. 180 = 80 + v2, so v2 = 100 km/hr.

Multiple choice

On a railway station platform, a boy is walking towards the enquiry window at a speed of 3 km/hr parallel to the railway line running alongside the platform. Meanwhile, a 150-metre long train running at a speed of 80 km/hr passes him, running in the same direction as the boy is walking. What is the time taken by the train to pass the boy?

  1. 4 seconds

  2. 5 seconds

  3. 6 seconds

  4. 7 seconds

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

Relative speed = 80 - 3 = 77 km/hr = 77 * (5/18) m/s = 385/18 m/s. Time = Distance / Speed = 150 / (385/18) = (150 * 18) / 385 = 2700 / 385 = 7.01 seconds.

Multiple choice

A train passes two persons who are walking in the direction opposite to the direction of train at the rate of 10 m/s and 20 m/s respectively in 12 seconds and 10 seconds, respectively. Find the length of the train.

  1. 400

  2. 500

  3. 600

  4. 700
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let L be the length of the train and v be its speed. The relative speed against the first person is (v + 10) and against the second is (v + 20). Using distance = speed * time, we have L = 12(v + 10) and L = 10(v + 20). Solving 12v + 120 = 10v + 200 gives 2v = 80, so v = 40. Substituting back, L = 12(40 + 10) = 600.

Multiple choice

A train passes a 100 meters long platform in 28 seconds and a man standing on the platform in 20 seconds. The speed of the train is: একটি ট্রেন একটি 100 মিটার লম্বা প্লাটফর্ম কে 28 সেকেন্ডে এবং প্লাটফর্মে দাঁড়িয়ে থাকা এক ব্যক্তি কে 20 সেকেন্ডে অতিক্রম করে তাহলে ট্রেনটিি দৈর্ঘ্য

  1. 45 km./hr

  2. 50 km./hr

  3. 60 km./hr

  4. 40 km./hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the train length be L metres and its speed be v metres per second. Passing a man gives L = 20v, while passing the platform gives L + 100 = 28v. Solving gives v = 12.5 m/s, which equals 45 km/h.

Multiple choice

The ratio of lengths of two trains P and Q is 3 : 5. Both the trains start running from the same station in the same direction but at different time interval. The time taken by train P to cross a tunnel whose length is 50% more than the sum of the lengths of the two trains is 46 minutes less than that by train Q. Find the length of tunnel. Speed of train P and Q is 72 km/hr and 54 km/hr respectively.

  1. 806

  2. 82.4

  3. 86.4

  4. 88.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let lengths be 3x and 5x. Tunnel length = 1.5 * (3x + 5x) = 12x. Speed P = 20 m/s, Speed Q = 15 m/s. Time P = (3x + 12x) / 20 = 15x / 20 = 0.75x. Time Q = (5x + 12x) / 15 = 17x / 15. Difference = 17x/15 - 0.75x = 46 minutes = 2760 seconds. (17x - 11.25x) / 15 = 2760 => 5.75x = 41400 => x = 7200. Tunnel = 12 * 7200 = 86400 meters = 86.4 km.

Multiple choice

A train is running at a speed of 48 km/hr. A passenger counts the telephone posts along the line as he passes them. If the posts are 50 m apart, then how many posts will he cross per minute? একটি ট্রেন 48 কিলোমিটার / ঘন্টা বেগে চলছে। কোনো যাত্রী টেলিফোনের পোস্টগুলি পাস করার সাথে সাথে গণনা করে। পোস্টগুলি যদি 50 মিটার দূরে থাকে তবে তিনি প্রতি মিনিটে কয়টি পোস্ট অতিক্রম করবেন?

  1. 17

  2. 20

  3. 24

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Ratio of the speed of two trains of length 270 m each is 4 : 5. While travelling in opposite directions, they cross each other in 12 seconds. What is the speed of faster train?

  1. 72 kmph

  2. 80 kmph

  3. 90 kmph

  4. 95 kmph

  5. 108 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The relative speed is total distance divided by time: (270 + 270) / 12 = 540 / 12 = 45 m/s. Converting to kmph, 45 * 18/5 = 162 kmph. With a speed ratio of 4:5, the faster train is 5/9 of the total relative speed: 5/9 * 162 = 90 kmph.

Multiple choice

A train 150m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speeds of the second train is:

  1. 60 kmph

  2. 66 kmph

  3. 72 kmph

  4. 99 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed of first train = 150m / 15s = 10 m/s = 36 km/hr. Relative speed of both trains = 150m + 150m / 8s = 300/8 = 37.5 m/s. Relative speed = 37.5 * 3.6 = 135 km/hr. Speed of second train = 135 - 36 = 99 km/hr.