TRAIN PROBLEMS – QUESTIONS, OPTIONS & EASY SOLUTIONS

0 0 gkloka Saturday, December 20, 2025 Edit this post

Train problems explained step by step with shortcuts. Perfect for SSC, Banking, PSI, FDA, KAS & competitive exams.

🚆 TRAIN PROBLEMS – MASTER ONCE, NEVER FORGET

🔑 GOLDEN RULES

✅ Rule 1: km/hr → m/sec conversion (Multiply by 5/18)

✅ Rule 2: m/sec → km/hr conversion (Multiply by 18/5)

✅ Rule 3 (VERY IMPORTANT):
• Crossing pole / man → Distance = Length of train
• Crossing platform / bridge → Distance = Train + Platform/Bridge

1️⃣ Question

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A) 120 metres
B) 180 metres
C) 324 metres
D) 150 metres

✏️ Solution (Step by Step)

Step 1: Convert speed (60 km/hr × 5/18 = 50/3 m/sec)

Step 2: Use formula (Distance = Speed × Time)

Length = (50/3) × 9 = 150 metres

✅ Correct Answer: D) 150 metres

2️⃣ Question

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A) 45 km/hr
B) 50 km/hr
C) 54 km/hr
D) 55 km/hr

✏️ Solution

Step 1: Distance = Length of train = 125 m

Step 2: Relative Speed = Distance / Time = 125/10 = 12.5 m/sec

Step 3: Convert to km/hr = 12.5 × 18/5 = 45 km/hr

Step 4: Relative Speed (Same direction) = Train Speed - Man Speed
45 = Train Speed - 5
Train Speed = 50 km/hr

✅ Correct Answer: B) 50 km/hr

3️⃣ Question

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

A) 200 m
B) 225 m
C) 245 m
D) 250 m

✏️ Solution

Step 1: Convert speed: 45 × 5/18 = 12.5 m/sec

Step 2: Total distance = Speed × Time = 12.5 × 30 = 375 m

Step 3: Bridge length = Total Distance - Train Length
375 - 130 = 245 m

✅ Correct Answer: C) 245 m

4️⃣ Question

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A) 1 : 3
B) 3 : 2
C) 3 : 4
D) None of these

✏️ Solution (Memory Trick)

Use Rule of Alligation:
Speed 1 time: 27 | Speed 2 time: 17
Mean time: 23
Ratio = |23-17| : |27-23|
Ratio = 6 : 4 = 3 : 2

✅ Correct Answer: B) 3 : 2

5️⃣ Question

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A) 120 m
B) 240 m
C) 300 m
D) None of these

✏️ Solution

Step 1: Convert speed: 54 × 5/18 = 15 m/sec

Step 2: Train length = Speed × Time (Man) = 15 × 20 = 300 m

Step 3: Total distance (Train + Platform) = 15 × 36 = 540 m

Step 4: Platform length = 540 - 300 = 240 m

✅ Correct Answer: B) 240 m

6️⃣ Question

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

A) 65 sec
B) 89 sec
C) 100 sec
D) 150 sec

✏️ Solution

Step 1: Find speed of train = 240/24 = 10 m/sec

Step 2: Total Distance = Train + Platform = 240 + 650 = 890 m

Step 3: Time required = Distance / Speed = 890 / 10 = 89 sec

✅ Correct Answer: B) 89 sec

7️⃣ Question

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

A) 50 m
B) 72 m
C) 80 m
D) 82 m

✏️ Solution

Step 1: Relative speed (same direction → subtract) = 46 - 36 = 10 km/hr

Convert to m/sec: 10 × 5/18 = 25/9 m/sec

Step 2: Total distance = Speed × Time = (25/9) × 36 = 100 m

Step 3: Since trains are equal length, Length of one train = 100 / 2 = 50 m

✅ Correct Answer: A) 50 m

8️⃣ Question

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

A) 40 sec
B) 42 sec
C) 45 sec
D) 48 sec

✏️ Solution

Step 1: Convert speed: 45 × 5/18 = 12.5 m/sec

Step 2: Total distance = Train + Bridge = 360 + 140 = 500 m

Step 3: Time = Distance / Speed = 500 / 12.5 = 40 sec

✅ Correct Answer: A) 40 sec

9️⃣ Question

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train is:

A) 36 sec
B) 45 sec
C) 48 sec
D) 49 sec

✏️ Solution

Step 1: Total Distance = 1.10 + 0.9 = 2.0 km = 2000 m

Step 2: Relative speed (opposite → add) = 60 + 90 = 150 km/hr

Convert to m/sec: 150 × 5/18 = 125/3 m/sec

Step 3: Time = Distance / Speed = 2000 / (125/3) = (2000 × 3) / 125 = 48 sec

✅ Correct Answer: C) 48 sec

🔟 Question

A jogger running at 9 km/hr is 240 metres ahead of the engine of a 120 metres long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

A) 3.6 sec
B) 18 sec
C) 36 sec
D) 72 sec

✏️ Solution

Step 1: Relative Speed (Same direction) = 45 - 9 = 36 km/hr

Convert: 36 × 5/18 = 10 m/sec

Step 2: Total Distance = Distance ahead + Train Length = 240 + 120 = 360 m

Step 3: Time = 360 / 10 = 36 sec

✅ Correct Answer: C) 36 sec

1️⃣1️⃣ Question

A 270 metres long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A) 230 m
B) 240 m
C) 260 m
D) 320 m

✏️ Solution

Step 1: Relative Speed (Opposite) = 120 + 80 = 200 kmph

Convert: 200 × 5/18 = 500/9 m/sec

Step 2: Total Distance = Speed × Time = (500/9) × 9 = 500 m

Step 3: Length of other train = 500 - 270 = 230 m

✅ Correct Answer: A) 230 m

1️⃣2️⃣ Question

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

A) 230 m
B) 240 m
C) 260 m
D) 270 m

✏️ Solution

Step 1: Convert speed: 72 × 5/18 = 20 m/sec

Step 2: Total Distance = 20 × 26 = 520 m

Step 3: Train length = 520 - 250 = 270 m

✅ Correct Answer: D) 270 m

1️⃣3️⃣ Question

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast as the other, then the speed of the faster train is:

A) 30 km/hr
B) 45 km/hr
C) 60 km/hr
D) 75 km/hr

✏️ Solution

Step 1: Total Distance = 100 + 100 = 200 m

Step 2: Relative Speed = 200 / 8 = 25 m/sec

Step 3: Let slower speed = x, Faster = 2x. Relative (Opposite) = 3x.

3x = 25 → x = 25/3 m/sec

Faster speed = 2x = 50/3 m/sec

Convert to km/hr: (50/3) × 18/5 = 60 km/hr

✅ Correct Answer: C) 60 km/hr

1️⃣4️⃣ Question

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other is:

A) 9
B) 9.6
C) 10
D) 10.8

✏️ Solution

Step 1: Total distance = 140 + 160 = 300 m

Step 2: Relative speed = 60 + 40 = 100 km/hr

Convert: 100 × 5/18 = 250/9 m/sec

Step 3: Time = 300 / (250/9) = (300 × 9) / 250 = 10.8 sec

✅ Correct Answer: D) 10.8 sec

1️⃣5️⃣ Question

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

A) 5 sec
B) 6 sec
C) 7 sec
D) 10 sec

✏️ Solution

Step 1: Relative Speed (Opposite) = 60 + 6 = 66 kmph

Convert: 66 × 5/18 = 55/3 m/sec

Step 2: Time = Distance / Speed = 110 / (55/3) = (110 × 3) / 55 = 6 sec

✅ Correct Answer: B) 6 sec

1️⃣6️⃣ Question

A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel?

A) 2.5 min
B) 3 min
C) 3.2 min
D) 3.5 min

✏️ Solution

Step 1: Total distance = 3.5 + 0.25 = 3.75 miles

Step 2: Speed = 75 mph

Step 3: Time = Distance / Speed = 3.75 / 75 = 0.05 hours

Step 4: Convert to minutes = 0.05 × 60 = 3 min

✅ Correct Answer: B) 3 min

1️⃣7️⃣ Question

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is:

A) 130
B) 360
C) 500
D) 540

✏️ Solution

Step 1: Convert speed: 78 × 5/18 = 65/3 m/sec

Step 2: Distance in 1 min (60 sec) = (65/3) × 60 = 1300 m

Step 3: Tunnel length = Total Distance - Train Length = 1300 - 800 = 500 m

✅ Correct Answer: C) 500

1️⃣8️⃣ Question

A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

A) 320 m
B) 350 m
C) 650 m
D) Data inadequate

✏️ Solution

Step 1: Speed = Length / Time (pole) = 300 / 18 = 50/3 m/sec

Step 2: Distance covered in 39 sec = (50/3) × 39 = 650 m

Step 3: Platform length = 650 - 300 = 350 m

✅ Correct Answer: B) 350 m

1️⃣9️⃣ Question

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A) 50 m
B) 150 m
C) 200 m
D) Data inadequate

✏️ Solution

Let Train Length = L

Speed = L/15 = (L+100)/25

25L = 15(L+100) → 25L = 15L + 1500

10L = 1500 → L = 150 m

✅ Correct Answer: B) 150 m

2️⃣0️⃣ Question

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

A) 69.5 km/hr
B) 70 km/hr
C) 79 km/hr
D) 79.2 km/hr

✏️ Solution

Let Length = L. Speed = L/8 = (L+264)/20

20L = 8L + (8 × 264) → 12L = 2112 → L = 176 m

Speed = 176 / 8 = 22 m/sec

Convert: 22 × 18/5 = 79.2 km/hr

✅ Correct Answer: D) 79.2 km/hr

2️⃣1️⃣ Question

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

A) 25
B) 30
C) 40
D) 45

✏️ Solution

Step 1: Relative speed (Same direction) = 63 - 3 = 60 km/hr

Convert: 60 × 5/18 = 50/3 m/sec

Step 2: Time = Distance / Speed = 500 / (50/3) = 30 sec

✅ Correct Answer: B) 30 sec

2️⃣2️⃣ Question

Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

A) 12 sec
B) 24 sec
C) 48 sec
D) 60 sec

✏️ Solution

Note: Passing driver means distance = length of slower train only (500m).

Step 1: Relative Speed = 45 + 30 = 75 km/hr

Convert: 75 × 5/18 = 125/6 m/sec

Step 2: Time = 500 / (125/6) = (500 × 6) / 125 = 24 sec

✅ Correct Answer: B) 24 sec

2️⃣3️⃣ Question

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

A) 10
B) 18
C) 36
D) 72

✏️ Solution

Step 1: Total Distance = 120 + 120 = 240 m

Step 2: Relative Speed = 240 / 12 = 20 m/sec

Step 3: Since speeds are same, Speed of one = 20 / 2 = 10 m/sec

Step 4: Convert: 10 × 18/5 = 36 km/hr

✅ Correct Answer: C) 36 km/hr

2️⃣4️⃣ Question

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train is 120 metres, in what time (in seconds) will they cross each other travelling in opposite directions?

A) 10
B) 12
C) 15
D) 20

✏️ Solution

Speed 1 = 120/10 = 12 m/s. Speed 2 = 120/15 = 8 m/s.

Relative Speed = 12 + 8 = 20 m/s.

Total Distance = 120 + 120 = 240 m.

Time = 240 / 20 = 12 sec.

✅ Correct Answer: B) 12 sec

2️⃣5️⃣ Question

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

A) 48 km/hr
B) 54 km/hr
C) 66 km/hr
D) 82 km/hr

✏️ Solution

Total Distance = 108 + 112 = 220 m. Time = 6 sec.

Relative Speed = 220 / 6 = 110/3 m/sec.

Convert Relative Speed: (110/3) × 18/5 = 132 km/hr.

Speed of second train = 132 - 50 = 82 km/hr.

✅ Correct Answer: D) 82 km/hr

2️⃣6️⃣ Question

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

A) 23 m
B) 23 2⁄9 m
C) 27 7⁄9 m
D) 29 m

✏️ Solution

Relative Speed = 40 - 20 = 20 km/hr.

Convert: 20 × 5/18 = 50/9 m/sec.

Distance (Length of fast train) = (50/9) × 5 = 250/9 = 27 7⁄9 m.

✅ Correct Answer: C) 27 7⁄9 m

2️⃣7️⃣ Question

A train overtakes two persons who are walking in the same direction at the rate of 2 km/hr and 4 km/hr and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A) 45 m
B) 50 m
C) 54 m
D) 72 m

✏️ Solution

Distance is same. 9(v-2) = 10(v-4). (Where v is train speed)

9v - 18 = 10v - 40 → v = 22 km/hr.

Relative speed 1: 22 - 2 = 20 km/hr = 20 × 5/18 = 50/9 m/sec.

Length = (50/9) × 9 = 50 m.

✅ Correct Answer: B) 50 m

2️⃣8️⃣ Question

A train overtakes two persons walking at 4.5 km/hr and 5.4 km/hr in the same direction. The train takes 8.4 sec and 8.5 sec respectively to overtake them. What is the speed of the train?

A) 66 km/hr
B) 72 km/hr
C) 78 km/hr
D) 81 km/hr

✏️ Solution

8.4(v - 4.5) = 8.5(v - 5.4)

8.4v - 37.8 = 8.5v - 45.9

0.1v = 8.1 → v = 81 km/hr.

✅ Correct Answer: D) 81 km/hr

2️⃣9️⃣ Question

A train travelling at 48 km/hr completely crosses another train having half its length and travelling in opposite direction at 42 km/hr in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is:

A) 400 m
B) 450 m
C) 560 m
D) 600 m

✏️ Solution

Rel Speed = 48 + 42 = 90 km/hr = 25 m/sec.

Total Len = 25 × 12 = 300m. Since L + L/2 = 300, 1.5L = 300 → L = 200m.

Train Speed = 48 km/hr = 40/3 m/sec.

Dist in 45s = (40/3) × 45 = 600m.

Platform = 600 - 200 = 400 m.

✅ Correct Answer: A) 400 m

3️⃣0️⃣ Question

Two stations A and B are 110 km apart. One train starts from A at 7 a.m. towards B at 20 km/hr. Another train starts from B at 8 a.m. towards A at 25 km/hr. At what time will they meet?

A) 9 a.m.
B) 10 a.m.
C) 10.30 a.m.
D) 11 a.m.

✏️ Solution

Step 1: 7am to 8am Train A covers 20km. Remaining dist = 110 - 20 = 90km.

Step 2: Rel Speed = 20 + 25 = 45 km/hr.

Step 3: Time = 90 / 45 = 2 hours.

Meeting time = 8 a.m. + 2 hours = 10 a.m.

✅ Correct Answer: B) 10 a.m.

3️⃣1️⃣ Question

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

A) 2 : 3
B) 4 : 3
C) 6 : 7
D) 9 : 16

✏️ Solution (SPECIAL SHORTCUT)

Formula: S1 : S2 = √T2 : √T1

Ratio = √16 : √9 = 4 : 3

✅ Correct Answer: B) 4 : 3