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 passenger train that runs at the speed of 78 km/h leaves the station 8 hours after the goods train left and overtakes it in 5 hours. What is the speed of goods train?

  1. 15

  2. 30

  3. 60

  4. 13

  5. 72
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let goods train speed = x km/h. Goods train travels for 8 + 5 = 13 hours before being overtaken. Passenger train speed = 78 km/h travels for 5 hours. Distance is same: 13x = 78 × 5 = 390. So x = 390 / 13 = 30 km/h. The key insight is that the goods train had an 8-hour head start, then both trains traveled for 5 more hours before the passenger train caught up.

Multiple choice

How much time will Train P take to cross Train Q (from the moment they meet) running in opposite directions (towards each other)? Statement I: The respective ratio of speeds of Train P and Train Q is 3: 4. The sum of the lengths of Train P and Train Q is 700 meters. Statement II: Train P can cross a signal pole in 12 seconds. It can cross 600-meter long stations in 25 seconds.

  1. Only I

  2. Both I and II

  3. Only II

  4. Either I or II

  5. Neither I nor II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II alone gives Train P's length and speed. From crossing a pole in 12s and 600m station in 25s, we can calculate P's length = L_P and speed = S_P. Using the station crossing: (L_P + 600) / S_P = 25, and L_P / S_P = 12, we can solve for both. Statement I gives speed ratio 3:4 and total length 700m. Combined with P's values from II, we get Q's speed and length. After meeting, crossing time = (L_P + L_Q) / (S_P + S_Q). Both statements together are necessary and sufficient.

Multiple choice

Two trains can cross a pole in 14 sec. and 16 sec. respectively. Find in how much time will they cross each other if they are coming from the same direction and if the speed of the trains are in the ratio of 7 : 9.

  1. 111 sec

  2. 119 sec.

  3. 131 sec.

  4. 121 sec.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speeds be 7x and 9x. Lengths are 7x×14 and 9x×16. Relative speed (same direction) = 9x - 7x = 2x. Time = (7x×14 + 9x×16)/(2x) = (98x + 144x)/(2x) = 242x/2x = 121 seconds.

Multiple choice

What is the speed of the train? I. The train crosses a signal pole in 13 sec. II. The train crosses a platform of length 250 m in 27 seconds. III. The train crosses another train running in the same direction in 32 seconds.

  1. I and II only

  2. I and III only

  3. II and III only

  4. Any two of the three

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

Let L = train length, s = speed. From I: L = 13s. From II: L + 250 = 27s. Combining: 13s + 250 = 27s, so 14s = 250, s = 125/7 ≈ 17.86 m/s. Statements I and II together are sufficient. Statement III mentions another train but doesn't give its length or speed, so it's insufficient alone or with only one other statement.

Multiple choice

Which information are necessary to answer the questions asked- At what time will the train reach point X from point Y? I. The train crosses another train of equal length of 250 m in 25 sec. running opposite direction. II. The train of 250 m crosses a signal pole in 10 sec. III. The distance between point X and point Y is 360 km.

  1. None of these

  2. II and III together are sufficient

  3. III and (I or II are sufficient)

  4. All three together are sufficient

  5. All three together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time = Distance / Speed. From II: Train's speed = 250m / 10s = 25 m/s. From III: Distance = 360 km = 360000 m. Time = 360000 / 25 = 14400s = 4 hours. Statement I about relative speed is unnecessary.

Multiple choice

Train P starts from point A at 10 am and runs at a constant speed of 60 km/hr on a straight track and reaches point B at a distance of 360km. Train Q starts from B at 11 am and runs towards A at some constant speed crosses train P at a distance of 120 km from B. what is the speed of train Q?(in km/hr)

  1. 40

  2. 30

  3. 50

  4. 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train P travels at 60 km/hr. Meeting point is 120 km from B, so it's 360-120=240 km from A. Train P takes 240/60=4 hours to reach meeting point, so they meet at 2 pm. Train Q travels from 11 am to 2 pm (3 hours) covering 120 km. Speed = 120/3 = 40 km/hr.

Multiple choice

Find the correct relationship between given quantities. A train passes another train coming from the opposite direction at a speed of 32 km/hr. Find the length of the train. Quantity I- Sum of lengths of both trains is 480 meter and its speed is 25% more than the speed of the other train. Quantity II- Difference of lengths of both trains is 80 meter and its speed is 25% less than the speed of the other train.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

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

This question has inconsistent information. If relative speed is 32 km/hr and one train is 25% faster than other, let slower = x, then 2.25x = 32, so x ≈ 14.2 km/hr. With sum = 480m and difference = 80m, lengths would be 280m and 200m. However, we also have that one train is 25% slower (different from being 25% faster). These conditions create inconsistency - we cannot determine a unique length that satisfies all constraints. Therefore, the relationship cannot be established.

Multiple choice

A train crosses a 110 m. long platform in 13.5 seconds and 205 m. long platform in 18.25 seconds. What was the speed of the train?

  1. 69 km/hr.

  2. 72 km/hr.

  3. 66 km/hr.

  4. 75 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let train length be L meters and speed be S m/s. For first platform: L+110 = S×13.5. For second platform: L+205 = S×18.25. Subtracting: (L+205) - (L+110) = S×(18.25-13.5) → 95 = 4.75S → S = 20 m/s = 72 km/hr. The train length is L = 20×13.5 - 110 = 160 m, but the question only asks for speed.

Multiple choice

Renu was sitting inside a train A, which was travelling at 50km/h, another train B whose length is three times the length of A crossed her in opposite direction in 15 second, if the speed of train B was 58 km/h , then the length of the train A is ( in m) is?

  1. 210

  2. 180

  3. 160

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

Relative speed of trains A and B = 50 + 58 = 108 km/h = 30 m/s. Train B crosses Renu in 15 seconds, so length of train B = 30 × 15 = 450 m. Since train B is three times the length of train A, length of train A = 450/3 = 150 m. Option D is correct.

Multiple choice

A 225 meters long train ‘P’ passed a pole in 6.75 sec. Train ‘P’ passed an another train ‘Q’ travelling in a direction opposite to ‘P’ in 60/7 sec. If length of train ‘Q’ is 375 meter, then in what time train ‘Q’ will pass train ‘P’ when they both runs in same direction ?

  1. 180 sec

  2. 280 sec

  3. 80 sec

  4. 168 sec

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

Train P speed = 225/6.75 = 100/3 m/s (33.33 m/s). Relative speed opposite direction = (225 + 375)/(60/7) = 600 × 7/60 = 70 m/s. So Q's speed = 70 - 100/3 = 110/3 m/s. Same direction relative speed = 110/3 - 100/3 = 10/3 m/s. Time to pass = (225 + 375)/(10/3) = 600 × 3/10 = 180 sec. Option A is correct.

Multiple choice

Train A can cross a man in 8 sec and a 180 m long platform ‘P’ in 17 sec. If train A cross train B which is running in opposite direction at speed of 108 km/hr in 8 sec, then find time (in sec) taken by train B to cross platform P?

  1. 12

  2. 15

  3. 18

  4. 14

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

Train A crosses man in 8s, so length L = speed_A * 8. Crosses 180m platform in 17s, so L+180 = speed_A * 17. Solving: speed_A * 17 - 180 = speed_A * 8, so speed_A * 9 = 180, speed_A = 20 m/s. Length L = 160m. Train B speed = 108 km/hr = 30 m/s. Relative speed (opposite) = 20+30 = 50 m/s. Crossing time = (L+LB)/50 = 8, so LB = 240m. Train B crosses platform: (240+180)/30 = 420/30 = 14s. Answer D is correct.

Multiple choice

A 220m long train crosses another 320m long train coming from opposite direction in 18 seconds . If the speed of the first train is 65 km/hr . What is the speed of another train .

  1. 43 km/hr

  2. 53 km/hr

  3. 63 km/hr

  4. 47 km/hr

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

When trains cross from opposite directions, relative speed = sum of individual speeds. Total distance covered = 220 + 320 = 540 m. Time = 18 seconds. Relative speed = 540/18 = 30 m/s = 108 km/hr. Speed of second train = 108 - 65 = 43 km/hr. This uses the relative speed concept for objects moving in opposite directions.

Multiple choice

A train crosses a pole in 12.5 seconds and crosses a platform of length 580 meter in 41.5 seconds . Then find the length of the train ?

  1. 280 meter

  2. 250 meter

  3. 350 meter

  4. 320 meter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let train length be L and speed be S. Crossing a pole takes 12.5 seconds: L = S × 12.5. Crossing a 580-meter platform takes 41.5 seconds: L + 580 = S × 41.5. Subtracting: (L + 580) - L = S × (41.5 - 12.5) → 580 = S × 29 → S = 20 m/s. Then L = 20 × 12.5 = 250 meters.

Multiple choice

A train traveling at a constant speed crosses two people running in the same direction in 10.8 seconds and 11.4 seconds, the first one is running at a speed of 4.8 km/hour while the other was at 6.6 km/hour. What is the speed of the train in km/hour?

  1. 39.6

  2. 40.2

  3. 38.4

  4. 39.0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train speed = v km/h and length = L km. For first person: L = (v - 4.8) × (10.8/3600). For second: L = (v - 6.6) × (11.4/3600). Equating: (v - 4.8) × 10.8 = (v - 6.6) × 11.4. Solving gives v = 39 km/h.