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 length 150 m each, takes 6 seconds to cross each other when they are travelling in opposite directions and take 30 seconds to cross each other when they are travelling in the same direction. Find the ratio of the speed of the faster train to that of slower train. 150 मीटर लंबी दो ट्रेनें विपरीत दिशाओं में यात्रा करते समय एक-दूसरे को पार करने में 6 सेकंड का समय लेती हैं और समान दिशा में यात्रा करते समय एक-दूसरे को पार करने में 30 सेकंड का समय लेती हैं। तेज ट्रेन की गति का धीमी ट्रेन की गति से अनुपात ज्ञात कीजिए।

  1. 3 :2

  2. 2:3

  3. 5:2

  4. 3:4

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

Let faster train speed = v₁ and slower train speed = v₂. When traveling in opposite directions, relative speed = v₁ + v₂, and they cover 300m (150 + 150) in 6 seconds: v₁ + v₂ = 300/6 = 50 m/s. When traveling in same direction, relative speed = v₁ - v₂, and they cover 300m in 30 seconds: v₁ - v₂ = 300/30 = 10 m/s. Adding equations: 2v₁ = 60, so v₁ = 30. Then v₂ = 20. Ratio v₁:v₂ = 30:20 = 3:2. Option B reverses the ratio.

Multiple choice

A train X travelling at 72 km/h crosses another train Y travelling at 63 km/h (in opposite direction) in 18 seconds. If the length of train Y is two-third the length of X, then length of train X is: एक ट्रेन X, 72 किमी/घंटा की गति से चल रही है, 63 किमी/घंटा (विपरीत दिशा में) से यात्रा कर रही दूसरी ट्रेन Y को 18 सेकंड में पार करती है। यदि ट्रेन Y की लंबाई X की लंबाई की दो-तिहाई है, तो ट्रेन X की लंबाई है:

  1. 300 m 300 मीटर

  2. 420 m 420 मीटर

  3. 405 m 405 मीटर

  4. 270 m 270 मीटर

  5. 525 m 525 मीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 72 + 63 = 135 km/h = 135×5/18 = 37.5 m/s. Crossing time = 18 sec. Total distance (sum of lengths) = 37.5 × 18 = 675 m. Let X's length = L. Then Y's length = (2/3)L. So L + (2/3)L = 675, (5/3)L = 675, L = 675 × 3/5 = 405 m.

Multiple choice

A goods train crosses a 150 meters long platform in 40 seconds and a man standing on the platform in 10 seconds. Find the length of the train.

  1. 100 m

  2. 50 m

  3. 175 m

  4. 150 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train length L, speed S. Crossing a man: L = 10S (train travels its own length in 10 sec). Crossing platform: L + 150 = 40S. Substituting: 10S + 150 = 40S, so 30S = 150, S = 5 m/s. Then L = 10 × 5 = 50 m. The train takes 10 seconds to pass a stationary point, so its speed equals its length/10.

Multiple choice

A train 250 meter 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?

  1. 15 sec

  2. 25 sec

  3. 18 sec

  4. 24 sec
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since both train and man move in same direction, relative speed = 68 - 8 = 60 km/hr. Converting to m/s: 60 × 1000/3600 = 50/3 m/s. The train must cover its own length (250 m) relative to the man. Time = Distance/Speed = 250 ÷ (50/3) = 250 × 3/50 = 15 seconds. Note: When objects move in same direction, subtract their speeds to get relative speed.

Multiple choice

A train of 300 -meter length crosses a platform of its double length in 30 second. Another train coming from opposite direction of length 350 meter with speed 90 km/hr cross first train in what second?

  1. 25

  2. 18

  3. 23

  4. 10

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

Train 1 length = 300m, platform = 600m (double length), total distance = 900m in 30s. Speed = 900/30 = 30 m/s = 108 km/hr. Train 2 (opposite direction) = 350m at 90 km/hr = 25 m/s. Combined speed = 108+90 = 198 km/hr = 55 m/s. Total distance = 300+350 = 650m. Time = 650/55 = 11.82 seconds. None of the options match.

Multiple choice

Two trains 200 m and 160 m long, run at the rate of 60 km/h and 100 km/h respectively on parallel rails. How long will it take a man sitting in the second train to pass the first train if they run in the opposite direction? 200 मीटर और 160 मीटर लंबी दो ट्रेनें समानांतर रेल पर क्रमशः 60 किमी/घंटा और 100 किमी/घंटा की दर से चलती हैं। विपरीत दिशा में चलने पर दूसरी ट्रेन में बैठे व्यक्ति को पहली ट्रेन को पार करने में कितना समय लगेगा?

  1. 4.5 seconds 4.5 सेकंड

  2. 4.9 seconds 4.9 सेकंड

  3. 6.4seconds 6.4सेकंड

  4. 8 seconds 8 सेकंड

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

The man sits in the second train (160 m, 100 km/h). When trains move in opposite directions, relative speed = sum of speeds = 60 + 100 = 160 km/h. Convert to m/s: 160 * (1000/3600) = 160 * (5/18) = 400/9 m/s. The man needs to pass the first train's length (200 m). Time = Distance / Speed = 200 / (400/9) = 200 * 9/400 = 9/2 = 4.5 seconds. This matches option A.

Multiple choice

A train crosses a pole in ‘n’ seconds and a platform which is 60% longer than train in 13 seconds. If the length of the platform is 120 meters, find the value of n?

  1. 6

  2. 8

  3. 5

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

Platform length = 120m. Platform is 60% longer than train, so train length = 120/1.6 = 75m. Train crosses platform in 13 seconds, so speed = (75+120)/13 = 195/13 = 15 m/s. Time to cross pole n = train length / speed = 75/15 = 5 seconds.

Multiple choice

A train has crossed a man in 7 seconds who is running on the platform with a speed of 5 km/hour in the opposite direction of the train. if the speed of the train is 31 km/hour then find the length of the train.

  1. 70 m

  2. 60 m

  3. 80 m

  4. 90 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative speed of the train with respect to the man running in opposite direction is 31 + 5 = 36 km/hr = 10 m/s. Since the train crosses the man in 7 seconds, the length of the train = relative speed × time = 10 × 7 = 70 m. When objects move in opposite directions, their speeds are added.

Multiple choice

Two trains P and Q of length 345 m and 635 m moving in the same direction with a speed of 33 km/hr and 82 km/hr respectively. In what time they cross each other?

  1. 20 sec

  2. 72 sec

  3. 32 sec

  4. 74 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When trains move in the same direction, their relative speed is the difference of their speeds: 82 - 33 = 49 km/hr, which converts to 49 × 5/18 = 245/18 m/s. The total distance to cross is the sum of lengths: 345 + 635 = 980 m. Time = distance / speed = 980 / (245/18) = 72 seconds. Option A (20 sec) would result from incorrectly adding speeds, while C and D are arithmetic errors.

Multiple choice

The speed of train A and train B is 93 km/hr and 51km/hr, respectively. When both the trains are running in the opposite direction, they cross each other in 18 seconds. The length of train B is half of the length of train A. If train A crosses a bridge in 42 seconds, then find the length of the bridge.

  1. 610 m

  2. 480 m

  3. 605 m

  4. 240 m

  5. 485 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed when moving opposite = 93 + 51 = 144 km/hr = 144 × (5/18) = 40 m/s. Total length (A + B) = 40 × 18 = 720 m. Let length of A = L, so B = L/2. Then L + L/2 = 720, giving L = 480 m. Length of B = 240 m. Train A crossing bridge at 93 km/hr = 93 × (5/18) = 155/6 m/s. Time = 42 sec, so distance covered = (155/6) × 42 = 1085 m. Bridge length = 1085 - 480 = 605 m.

Multiple choice

A train of 245-meter length crosses a platform of its double length in 45 second. Another train coming from opposite direction of length 364 meter with speed 63 km/hr cross first train in what second?

  1. 12 sec

  2. 15 sec

  3. 14 sec

  4. 11 sec

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

Train 1 length = 245m, platform length = 2×245 = 490m. Total distance = 245+490 = 735m. Time = 45 seconds. Train 1 speed = 735/45 = 16.33 m/s = 58.8 km/hr ≈ 59 km/hr. Train 2 length = 364m, speed = 63 km/hr. When crossing in opposite directions, relative speed = 59+63 = 122 km/hr = 33.89 m/s. Total distance to cross = 245+364 = 609m. Time = 609/33.89 = 17.97 seconds ≈ 18 seconds. This matches none of the options A-D, so E (None of these) is correct.

Multiple choice

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: How much time will the train A take to cross another train B running in opposite direction? I. Train A crosses a signal pole in 18s II. Ratio of the speed of trains A and B is 3:5 III. Length of two trains together is 1100m

  1. Only I

  2. All the given statements are Insufficient

  3. Only I and II

  4. Only III

  5. Only II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find crossing time in opposite direction, we need total length and relative speed. Statement I gives L_A/V_A = 18 (one equation, two unknowns). Statement II gives V_B = (5/3)V_A. Statement III gives L_A + L_B = 1100m. Combining all: Time = (L_A + L_B) / (V_A + V_B) = 1100 / ((8/3)V_A). But V_A remains unknown since we have L_A = 18V_A and L_A + L_B = 1100, which doesn't help isolate V_A. The system is underdetermined.

Multiple choice

The ratio of lengths of Train A and Train B is 2 : 3. The speed of A is 36 km/h and that of B is 54 km/h. They cross each other completely in 10 seconds when travelling in opposite directions. In how much time (in seconds) does Train B cross completely a tunnel of length 450 m?

  1. 35

  2. 38

  3. 42

  4. 40
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let lengths be 2x and 3x. Relative speed = 36+54=90 km/h = 25 m/s. Time to cross = (2x+3x)/25 = 5x/25 = 10s, so x=50. Lengths: A=100m, B=150m. Speed of B = 54 km/h = 15 m/s. Tunnel crossing time = (150+450)/15 = 600/15 = 40 seconds.