Train Problems - Key Formulas
Train Passing a Stationary Object
Time = Length of train / Speed of train
Train Passing a Platform/Station
Time = (Length of train + Length of platform) / Speed of train
Two Trains Crossing Each Other
Same Direction: Time = (L1 + L2) / |S1 - S2|
Opposite Direction: Time = (L1 + L2) / (S1 + S2)
Speed Conversion
km/hr to m/s: Multiply by 5/18
m/s to km/hr: Multiply by 18/5
Train Problems
Practice aptitude questions on trains, speed, time, and distance
Question 1:
A train with a speed of 120kmph passes a man in 15 seconds. Find the length of the train.
The speed of the train in meter per second = 120 * 1000 / 3600 = 120 * 5 / 18 = 600 / 18 = 100 / 3 m/s
The time taken by the train to travel through the man = 15 seconds
The length of the train = 100 * 15 / 3 = 500 m.
Question 2:
A train with a speed of 45kmph passes a man in 20 seconds. Find the length of the train.
The speed of the train in meters per second = 45 * 5 / 18 = 25 / 2 m/s
The time taken by the train to pass through the man = 20 seconds
The length of the train = 20 * 25 / 2 = 250m.
Question 3:
A train with length of 50 m passes a man in 3 seconds. Find the speed of the train.
The distance covered by the train = the length of the train
The distance covered = 50m
The time taken = 3 seconds
The speed = 50 / 3 m/s = 50 / 3 * 3600 / 1000 = 50 * 18 / (5 * 3) = 60 kmph.
Question 4:
A train 150 m in length passes a man in 12 seconds. Find the speed of the train.
The distance to be covered = the length of the train
The distance to be covered = 150m
The time taken = 12 seconds
The speed = 150 / 12 = 25 / 2 m/s
The speed = 25 / 2 * 18 / 5 kmph = 45 kmph.
Question 5:
The speed of a train is 120 kmph and the length of the train is 240 m. Find the time it will take to cross a pole.
The distance to be covered = 240 m
The speed = 120 kmph
The speed in meter per second = 120 * 5 / 18 = 100 / 3
The time taken = 240 / 100 * 3 = 7.2 seconds.
Question 6:
A train with length 300m crosses a pole at a speed of 50 kmph. Find the time taken by the train to cross the pole.
The speed of the train = 50 kmph = 50 * 5 / 18 meter per second = 125 / 9 m/s
The distance to be covered = 300 m
The time taken to cross 300m = 300 / 125 * 9 = 108 / 5 seconds = 21.6 seconds.
Question 7:
A train is 315 m in length and crosses a pole in 27 seconds. Find the speed of the train.
The distance to be covered = the length of the train
The distance to be covered = 315 m
The time taken = 27 seconds
The speed of the train = 315 / 27 m/s = 35 / 3 m/s = 35 / 3 * (18 / 5) = 42 kmph.
Question 8:
A train 405 m in length passes a pole in 45 seconds. Find the speed of the train.
The distance to be covered = the length of the train
The distance to be covered = 405 m
The time taken = 45 seconds
The speed of the train = 405 / 45 = 9 m/s
The speed = 9 * 18 / 5 = 32.4 kmph.
Question 9:
A train moving at a speed of 25 kmph crosses a pole in 9 seconds. Find the length of the train.
The length of the train = the distance covered
The distance covered = speed * time = 25 * 9 / 3600 km = 25 * 5 / 18 * 9 m = 62.5 m.
Question 10:
A train covers 120 km in 480 minutes. Find the speed of the train.
The speed of the train = distance / time = 120 / 480 = 0.25 km/minute = 15 kmph
The speed in meter/second = 15 * 5 / 18 = 4.16 m/s.
Question 11:
A train crosses a station of 400 m in 20 seconds running at a speed of 198 kmph. Find the length of the train.
The speed of the train in meter per second = 55 m/s (198 * 5 / 18)
The distance covered by the train = 55 * 20 = 1100 m
The length of the train = total distance covered – the length of the platform = 1100 – 400 = 700 m
Question 12:
A train 500 m in length crosses a station in 25 seconds travelling at a speed of 144 kmph. Find the length of the station.
The distance covered = time * speed = 25 * 40 = 1000 m (144 kmph = 40 m/s)
The length of the station = total distance – length of the train = 1000 – 500 = 500 m
Question 13:
A train with a length of 120m crosses a platform in 10 seconds. If the speed of the train is 90 kmph, find the length of the station.
The speed of the train = 90 kmph = 25 m/s
The total distance travelled = 25 * 10 = 250 m
The length of the platform = 250 – 120 = 130 m
Question 14:
A train crossed a station in 13 seconds with a speed of 46.8 kmph. Find the combined length of the train and the station.
The combined length of the train and the station = the total distance covered
The total distance covered = speed * time
Speed = 46.8 kmph = 13 m/s
Distance = 13 * 13 = 169 m
Question 15:
A train passes a station in x seconds at a speed of 194.4 kmph. If the combined length of the train and the station is 1200 m, find x.
The total distance travelled = 1200 m = 1.2 km
The total time taken = distance / speed = 1.2 / 194.4 = 1 / 162 hours = 22.22 seconds
Question 16:
A train crosses a station in 35 seconds. Find the length of the station if the train passes the station at a speed of 12 m/s. The train is equal to the station in length.
The total distance covered = 35 * 12 = 420 m
The length of the station = the length of the train = 420 / 2 = 210 m
Question 17:
A train 0.3 km in length passes a platform 500m long in 5 seconds. Find the speed of the train.
The total distance covered = 800 m
The total time taken = 5 seconds
The speed = 160 m/s = 576 kmph
Question 18:
A train with a speed of 10.08 kmph passes a platform in 12 seconds. Find the length of the platform if the train is 20 m long.
The total distance travelled = speed * time = 12 * 2.8 = 33.6 m
The length of the platform = 33.6 – 20 = 13.6 m
Question 19:
A train crosses a platform in 12.23 seconds. If the speed of the train is 44.028 kmph, find the combined length of the train and the platform.
The combined length = the total distance covered
The total distance covered = speed * time = 12.23 * 12.23 = 149.5729 m ≈ 150 m
Question 20:
A train passes a platform in 49 seconds. Find the length of the train if the length of the platform is 150 m and the speed of the train is 79.2 kmph.
The total distance = speed * time = 49 * 22 = 1078 m
The length of the train = 1078 – 150 = 928 m
Question 21:
A train 250 m in length crossed a station 500 m in length in 45 seconds, find the time needed by the train to cover 50 km.
The speed of the train = distance / time = 750 / 45 = 16.66 m/s
The speed in kmph = 60 kmph
The time taken to cover 50 km = 50 / 60 = 0.83 hours.
Question 22:
A train 350m long crossed a station of equal length in 105 seconds. Find the time required by the train to cover 1270 km.
The speed of the train = distance / time = 700 / 105 = 6.66 m/s = 24 kmph
Time taken to cover 1270 km = 1270 / 24 = 52.916 hours.
Question 23:
The speed of a train is 45 kmph. Find the time required by the train to cross a station of 500m if the train is 340m long.
The speed of the train = 45 kmph = 12.5 m/s
The time required = (500 + 340) / 12.5 = 840 / 12.5 = 67.2 minutes = 1.12 hours.
Question 24:
A train is x meters long. The train crosses a station 5x meters long in 40 seconds. Find the speed of the train in terms of x.
The speed of the train = distance covered / time taken = (5x + x) / 40 = 6x / 40 m/s = 6x * 18 / 40 * 5 = 108x / 200 kmph = 27x / 50 kmph.
Question 25:
A train with a speed of 12.5 kmph crosses a station 125 m long in 125 seconds. Find the length of the train.
The total distance covered = speed * time
Speed of the train = 12.5 kmph = 3.472 m/s
The distance = 3.472 * 125 = 434 m
The length of the train = 434 – 125 = 309 m.
Question 26:
The distance covered by a train in 87 minutes is 108.75 km. find the time taken by the train to cross a platform equal to its length. The train is 450 m long.
The speed of the train:
The speed = distance / time = 108.75 / 87 = 1.25 km per minute = 75 kmph = 20.83 m/s
The total distance to be covered = 450 * 2 = 900m
The time taken = 900 / 20.83 = 40.206 seconds.
Question 27:
The time taken by a train to cover a distance equal to its length is 120 seconds. If the speed of the train is 45 kmph, find the length of the train.
The speed of the train = 45 kmph = 12.5 m/s
The distance covered = Let it be 2x.
The distance = Speed * time = 120 * 12.5 = 1500
2x = 1500 m
X = 1500 / 2 = 750 m
Question 28:
The distance covered by a train in 6 hours is 1260 km. Find the time taken by the train to cross a station 3 km long. The train is 245m long.
The speed of the train = distance / time = 1260 / 6 = 210 kmph
The speed = 210 kmph = 58.33 m/s
The distance to be covered = 3000m + 245m = 3245m
The time taken = 3245 / 58.33 = 55.63 seconds.
Question 29:
A train 750m long travels through a tunnel 12 km long in 1250 seconds. Find the speed of the train.
The speed of the train = distance / time
The distance = 1200m + 750m = 12750 m or 12.75 km
The speed of the train = 12750 / 1250 = 10.2 m/s = 36.72 kmph.
Question 30:
A train 120 m in length crosses a tunnel 9 km long in 1338 seconds. Find the speed of the train.
The total distance to be covered = 9000m + 120m = 9120m
The time taken = 9120
The speed of the train = 9120 / 1338 = 6.816 m/s = 24.5 kmph.
Question 31:
Two trains cross each other at a speed of 50 kmph and 55 kmph, respectively. If the total length of both the trains is 1200m, find the time in which they crossed each other. The trains were moving in the same direction.
The trains moving in the same direction: The relative speed = 55 – 50 = 5 kmph
The distance to be covered = 1200 m = 1.2km
The time taken = 1.2 / 5 = 0.24 hours = 14.4 minutes.
Question 32:
Two trains cross each other at a speed of 50 kmph and 55 kmph, respectively. If the total length of both the trains is 1200m, find the time in which they crossed each other. The trains were moving in the opposite direction.
The relative speed = 55 + 50 = 105 kmph
The total distance = 1.2 km
The time taken = 1.2 / 105 = 0.0114 hours = 41.14 seconds.
Question 33:
Two trains cross each other at a speed of 30kmph and 45 kmph, respectively. If they are moving in the same direction, find the length of both the trains combined. The time taken = 12 seconds.
The total distance travelled = speed * time
The relative speed = 45 – 30 = 15 kmph = 4.16 m/s
The total distance = 12 * 4.16 = 49.92 m.
Question 34:
Two trains cross each other at a speed of 30kmph and 45 kmph, respectively. If they are moving in the opposite direction, find the length of both the trains combined. The time taken = 12 seconds.
The relative speed = 30 + 45 = 75 kmph = 20.83 m/s
The distance covered = 12 * 20.83 = 249.96 m = 0.25 km.
Question 35:
Two trains cross each other at a speed of 40 kmph and 60 kmph, respectively. Find the combined distance of both the trains if the time taken is 20 seconds and the trains move in the same direction.
The relative speed = 60 – 40 = 20 kmph = 5.55 m/s
The total distance covered = 20 * 5.55 = 111 m.
Question 36:
Two trains cross each other at a speed of 40 kmph and 60 kmph, respectively. Find the combined distance of both the trains if the time taken is 20 seconds and the trains move in the opposite direction.
The relative speed = 40 + 60 = 100 kmph = 27.77 m/s
The total distance covered = 27.77 * 20 = 555.4 m.
Question 37:
Two trains cross each other in 23 seconds. Find the length of both the trains combined if the speeds of the trains are 56 kmph and 76 kmph, respectively. The trains were moving in the same direction.
The relative speed = 76 – 56 = 20 kmph = 5.55 m/s
The total distance covered = 5.55 * 23 = 127.65 m.
Question 38:
Two trains cross each other in 23 seconds. Find the length of both the trains combined if the speeds of the trains are 56 kmph and 76 kmph, respectively. The trains were moving in the opposite direction.
The relative speed = 56 + 76 = 132 kmph = 36.66 m/s
The total distance covered = 36.66 * 23 = 843.18 m.
Question 39:
2 trains cross each other in 78 seconds. The speeds of the trains are 89 kmph and 69 kmph, respectively. Find the combined length of both the trains. The trains are moving in the same direction.
The relative speed = 89 – 68 = 20 kmph = 5.55 m/s
The total distance covered = 5.55 * 78 = 432.9 m ≈ 433 m.
Question 40:
2 trains cross each other in 28 seconds. If the speeds of the trains are 89 kmph and 69 kmph, respectively. Find the combined length of both the trains. The trains are moving in the opposite direction.
The relative speed = 89 + 69 = 158 kmph = 43.88 m/s
The total distance covered = 43.88 * 28 = 1228.64 m ≈ 1.23 km.
Question 41:
Two trains crosses each other in 9 seconds travelling in the opposite direction. Find the combined length of the trains if their speeds are 76 kmph and 63 kmph.
The relative speed = 76 + 63 = 139 kmph = 38.61 m/s
The distance covered = 38.61 * 9 = 347.49 m.
Question 42:
Two trains crosses each other in 99 seconds travelling in the same direction. Find the combined length of the trains if their speeds are 76 kmph and 63 kmph.
The relative speed = 76 – 63 = 13 kmph = 3.611 m/s
The total distance covered = 99 * 3.611 = 357.489 m.
Question 43:
Two trains cross each other at speed 57 kmph and 87 kmph. If both the trains move in the same direction, find the combined length of the trains. The time taken by the train to cross each other is 85 seconds.
The relative speed = 87 – 57 = 30 kmph = 8.33 m/s
The total distance covered = 8.33 * 85 = 708.05 m.
Question 44:
Two trains cross each other at speed 57 kmph and 87 kmph. If both the trains move in the opposite direction find the combined length of the trains. The time taken by the train to cross each other is 15 seconds.
The relative speed = 57 + 87 = 144 kmph = 40 m/s
The total distance covered = 40 * 15 = 600 m.
Question 45:
Two trains cross each other at a speed of 120 kmph and 145 kmph. If they move in the same direction and take 50 seconds to cross each other, find the combined length of both the trains.
The relative speed = 145 – 120 = 25 kmph = 6.94 m/s
The total distance covered = 6.94 * 50 = 347 m.
Question 46:
Two trains cross each other at a speed of 120 kmph and 145 kmph. If they move in the opposite direction and take 9 seconds to cross each other, find the combined length of both the trains.
The relative speed = 120 + 145 = 265 kmph = 73.61 m/s
The total distance covered = 73.61 * 9 = 662.49 m.
Question 47:
Two trains cross each other at a speed of 93 kmph and 65 kmph. If both the trains move in the same direction and take 56 seconds to cross each other, find the combined length of the trains.
The relative speed of the trains = 93 – 65 = 28 kmph = 7.77 m/s
The total distance covered = 7.77 * 56 = 435.12 m.
Question 48:
Two trains cross each other at a speed of 93 kmph and 65 kmph. If both the trains move in the opposite direction and take 17 seconds to cross each other, find the combined length of the trains.
The relative speed = 93 + 65 = 158 kmph = 43.88 m/s
The total distance covered = 43.88 * 17 = 745.96 m.
Question 49:
Two trains cross each other in 143 seconds with a speed of 123 kmph and 154 kmph. Find the length of the trains combined if the trains are moving in the same direction.
The relative speed = 154 – 123 = 31 kmph = 5.83 m/s
The total distance covered = 5.83 * 143 = 833.69 m.
Question 50:
Two trains cross each other in 13 seconds with a speed of 123 kmph and 154 kmph. Find the length of the trains combined if the trains are moving in the opposite direction.
The relative speed = 123 + 154 = 277 kmph = 76.94 m/s
The total distance covered = 76.94 * 13 = 1000.22 m.
Question 51:
A train moving with a speed of 23 kmph passes a pole in 12.9 seconds. Find the length of the train.
Speed = 23 kmph = 6.38 m/s
Length = 6.38 × 12.9 = 82.302 m
Question 52:
A train moving at a speed of 58 kmph passes a pole in 7.4 seconds. Find the length of the train.
Speed = 58 kmph = 16.11 m/s
Length = 16.11 × 7.4 = 119.214 m
Question 53:
A train moving with a speed of 73 kmph passes a man walking with a speed of 7 kmph in the same direction in 32 seconds. Find the length of the train.
Relative speed = (73 - 7) = 66 kmph = 18.33 m/s
Length = 18.33 × 32 = 586.56 m
Question 54:
A train with a speed of 113 kmph passes a man with a speed of 104 kmph moving in the same direction in 98 seconds. Find the length of the train.
Relative speed = (113 - 104) = 9 kmph = 2.5 m/s
Length = 2.5 × 98 = 245 m
Question 55:
A train with a speed of 113 kmph passes a man with a speed of 104 kmph moving in the opposite direction in 9 seconds. Find the length of the train.
Relative speed = (113 + 104) = 217 kmph = 60.27 m/s
Length = 60.27 × 9 = 542.43 m
Question 56:
A train moving with a speed of 73 kmph passes a man walking with a speed of 7 kmph in the opposite direction in 3.2 seconds. Find the length of the train.
Relative speed = (73 + 7) = 80 kmph = 22.2 m/s
Length = 22.2 × 3.2 = 71.04 m
Question 57:
A train crosses a pole at a speed of 12 kmph in 123 seconds. Find the length of the train.
Speed = 12 kmph = 3.33 m/s
Length = 3.33 × 123 = 409.59 m
Question 58:
A train crosses a pole at a speed of 24 kmph in 15 seconds. Find the length of the train.
Speed = 24 kmph = 6.66 m/s
Length = 6.66 × 15 = 99.9 m
Question 59:
A train covers 6 km in 12 minutes. Find the length of the train if it passes a pole in 12 seconds.
Speed = (6 / 12) km/min = 0.5 km/min = 30 kmph = 8.33 m/s
Length = 8.33 × 12 = 99.96 m
Question 60:
A train crosses a man in 7 seconds. If the length of the train is 763m, find the speed of the train.
Speed = 763 / 7 = 109 m/s = 392.4 kmph